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Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions

Important Questions for Class 10 Maths Chapter 5 Arithmetic Progressions with solutions includes all the important topics with detailed explanation that aims to help students to score more marks in Board Exams 2020. Students who are preparing for their Class 10 exams must go through Important Questions for Class 10 Math Chapter 5 Arithmetic Progressions.

Important Questions for Class 10 Maths Chapter 5 Arithmetic Progressions

Expert teachers at CBSETuts.com collected and solved 2 Marks and 4 mark important questions for Class 10 Maths Chapter 5 Arithmetic Progressions. All the solutions given in this page are solved based on CBSE marking scheme and NCERT guidelines.

2016

Very Short Answer Type Questions [1 Mark]

Question 1.
Find the 9th term from the end (towards the first term) of the A.P. 5, 9,13,185.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 1

Question 2.
For what value of k will k + 9,2k -1 and 2k + 7 are the consecutive terms of an A.P.?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 2

Question 3.
For what value ofk will the consecutive terms 2k + 1, 3k + 3 and 5k -1 form an A.P.?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 3

Short Answer Type Questions I [2 Marks]

Question 4.
How many terms of the A.P. 18,16,14,… be taken so that their sum is zero?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 4
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 5

Question 5.
How many terms of the A.P. 27,24,21,… should be taken so that their sum is zero?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 6

Question 6.
How many terms of the A.P. 65,60, 55,… be taken so that their sum is zero?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 7

Question 7.
The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 8

Question 8.
If the ratio of sum of the first m and n terms of an A.P. is m2 : n2 , show that the ratio of its mth and nth terms is (2m -1): (2n -1).
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 9

Short Answer Type Questions II [3 Marks]

Question 9.
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 10

Question 10.
If the ratio of the sum of first n terms of two A.P.’s is (7n + 1): (4n + 27), find the ratio of their mth terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 11

Question 11.
The digits of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 12

Question 12.
The sums of first n terms of three arithmetic progressions are S1, S2 and S3 respectively. The first term of each A.P. is 1 and their common differences are 1,2 and 3 respectively. Prove that S2 + S3 = 2Sr
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 13
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 14

Question 13.
Divide 56 in four parts in A.R such that the ratio of the product of their extremes (1st and 4th) to the product of means (2nd and 3rd) is 5 : 6.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 15

Question 14.
The pih, 9th and rth terms of an A.P. are a, b and c respectively. Show that a(q – r) + b(r-p) + c(p – q) = 0
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 16
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 17

Question 15.
The sums of first n terms of three A.Ps’ are S1, S2 and S3. The first term of each is 5 and their common differences are 2,4 and 6 respectively. Prove that S1 + S3 = 2Sr
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 18

Question 16.
A thief runs with a uniform speed of 100 m/minute. After one minute a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 19
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 20

Question 17.
A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 21

Question 18.
The sum of three numbers in A.P. is 12 and sum of their cubes is 288, Find the numbers.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 22
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 23

Question 19.
The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proceding the house numbered X is equal to sum of the numbers of houses following X.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 24

Question 20.
Reshma wanted to save at least ? 6,500 for sending her daughter to school next year (after 12 months). She saved ? 450 in the first month and raised her savings by ? 20 every next month. How much will she be able to save in next 12 months? Will she be able to send her daughter to the school next year?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 25

2015

Very Short Answer Type Question [1 Mark]

Question 21.
Find the 25th term of the A.P. – 5, -5/2, 0, 5/2……………
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 26

Short Answer Type Questions I [2 Marks]

Question 22.
Find the middle term of the AP 6,13,20,…, 216.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 27
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 28

Question 23.
Find the middle term of the AP 213,205,197,…, 37.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 29

Question 24.
In an AP, if S5 + S7 = 167 and S10 = 235, then find the AP, where Sn denotes the sum of its first n terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 30

Question 25.
The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 31

Question 26.
The fifth term of an A.P. is 20 and the sum of its seventh and eleventh terms is 64. Find the common difference of the A.P.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 32
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 33

Question 27.
The ninth term of an A.P is -32, and the sum of eleventh and thirteenth terms is -94.find the common difference of the A.P
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 34

Short Answer Type Questions

Question 28.

Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 35

Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 36

Question 29.
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 37
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 38

Question 30.
It Sn, denotes the sum of first n-terms of an AP. Prove that: S12 = 3 (S8 – S4)
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 39

Question 31.
The 14th term of an AP is twice its 8th term. If its 6th term is -8, then find the sum of its first 20 terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 40

Question 32.
The 16th term of an AP is five times its third term. If its 10th term is 41, then find the sum of its first fifteen terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 41

Question 33.
The 13th term of an AP is four times its 3rd term. If its fifth term is 16, then find the sum of its first ten terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 42
Question 34.
In an A.P., if the 12th term is -13 and the sum of its first four terms is 24, find the sum of its first ten terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 43

Long Answer Type Questions [4 Marks]

Question 35.
Ramkali required ? 2500 after 12 weeks to send her daughter to school. She saved t 100 in the first week and increased her weekly saving by ? 20 every week. Find whether she will be able to send her daughter to school after 12 weeks or not. What value is generated in the above situation?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 44

Question 36.
Find the 60th term of the AP 8,10,12,…, if it has a total of 60 terms and hence find the sum of its last 10 terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 45

Question 37.
An arithmetic progression 5,12,19,… has 50 terms. Find its last term. Hence find the sum of its last 15 terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 46

Question 38.
Find the middle term of the sequence formed by all three-digit numbers which leave a remainder 3, when divided by 4. Also find the sum of all numbers on both sides of the middle terms separately.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 47

Question 39.
Find the middle term of the sequence formed by all numbers between 9 and 95, which leave a remainder 1 when divided by 3. Also find the sum of the numbers on both sides of the middle term separately.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 48

Question 40.
Find the middle term of the sequence formed by all three-digit numbers which leave a remainder 5 when divided by 7. Also find the sum of all numbers on both sides of the middle term separately.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 49

2014

Short Answer Type Questions I [2 Marks]

Question 41.
The first and the last terms of an AP are 8 and 65 respectively. If sum of all its terms is 730, find its common difference.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 50

Question 42.
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 51
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 52

Question 43.
The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 53

Question 44.
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 54

Question 45.
The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 55
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 56

Question 46.
The sum of the first n terms of an AP is 5n – n2. Find the nth term of this AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 57

Question 47.
The sum of the first n terms of an AP is 4n2 + 2n. Find the nth term of this AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 58

Short Answer Type Questions II [3 Marks]

Question 48.
If the seventh term of an AP is and its ninth term is , find its 63rd term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 59

Question 49.
The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is I less than twice its 8th term, find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 60

Question 50.
The sum of the first seven terms of an AP is 182. If its 4tji and the 17th terms are in the ratio 1: 5, find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 61

Question 51.
The sum of the 5th and the 9th terms of an AP is 30. If its 25th term is three times its 8th term, find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 62
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 63

Question 52.
The sum of the first 7 terms of an AP is 63 and the sum of its next 7 terms is 161.Find the 28th term of this AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 64

Long Answer Type Questions [4 Marks]

Question 53.
In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 65

Question 54.
In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students. Which value is shown in this question?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 66

Question 55.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20-S10)
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 67

2013

Short Answer Type Questions

Question 56.
How many three digit natural numbers are divisible by 7?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 68

Question 57.
Find the number of all three-digit natural numbers which are divisible by 9.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 69

Question 58.
Find the number of three-digit natural numbers which are divisible by 11
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 70

Short Answer Type Questions II [3 Marks]

Question 59.
Find the number of terms of the AP: 18,15. 1/2, 13……..(-49. 1/2),and find the sum of all its terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 71

Question 60.
The nth term of an AP is given by (-4n + 15). Find the sum of first 20 terms of this A.Progressions
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 72

Question 61.
The sum of first n-terms of an AP is 3n2 + 4n. Find the 25th term of this AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 73

Question 62.
The 8th term of an AP is equal to three times its 3rd term. If its 6th term is 22, find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 74

Question 63.
The 9th term of an AP is equal to 6 times its 2nd term. If its 5th term is 22, find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 75
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 76

Question 64.
The 19th term of an AP is equal to three times its 6th term. If its 9th term is 19, find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 77

Question 65.
The 8th term of an AP is 31. If its 15th term exceeds its 11th term by 16, find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 78

Question 66.
The 18th term of an AP is 30 more than its 8th term. If the 15th term of the AP is 48, find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 79

Question 67.
The 5th term of an AP exceeds its 12th term by 14. If its 7th term is 4, find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 80

Long Answer Type Questions [4 Marks]

Question 68.
Find the number of terms of the AP – 12, -9,-6, … 21. If 1 is added to each term of this AP, then find the sum of all terms of the AP thus obtained. [Delhi]
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 81

Question 69.
The 24th term of an AP is twice its tenth term. Show that its 72nd term is 4times its 15th term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 82

Question 70.
If the sum of first 7 terms of an AP is 49 and that of first 17 terms 289. find the sum of its first n terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 83

Question 71.
The sum of first m terms of an AP is 4m2 – m. If its n. Also, find the 21st term of this AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 84

Question 72.
The sum of first q terms of an AP is 63q – 3q2. If its pth term is -60, find the value of p. Also find the 11th term of this AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 85
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 86

Question 73.
Students of a school thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees and so on till class XII. There are three sections of each class. Find the total number of trees planted by the students of the school.
Pollution control is necessary for everybody’s health. Suggest one more role of students in it.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 87

2012

Short Answer Type Questions I [2 Marks]

Question 74.
Find the sum of all three digit natural numbers, which are multiples of 11.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 88

Question 75.
Find the sum of all three digit natural numbers, which are multiples of 9.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 89

Question 76.
Find the sum of all three digits natural numbers, which are multiples of 7.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 90

Question 77.
How many three digit numbers are divisible by 11?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 91

Question 78.
How many three-digit numbers are divisible by 12?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 92

Question 79.
In an AP, the first term is 12 and the common difference is 6. If the last term of the A.P. is 252, find its middle term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 93

Question 80.
In an A.P., the first term is 8 and the common difference is 7. If the last term of the A.P. is 218, find its middle term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 94

Question 81.
In an A.P., the first term is 5 and the common diference is 2. If the last term of the A.P. is 53, find its middle term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 95

Short Answer Type Questions Il [3 Marks]

Question 82.
The 15th term of an A.P. is 3 more than twice its 7th term. If the 10th term of the A.P. is 41, then find its nth term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 96

Question 83.
The 17th term of an A.P. is 5 more than twice is 8th term, if the 11th term of the A.P. is 43, then find its nth term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 97

Question 84.
The 16 term of an A.P. is 1 more than twice its 8th term. If the 12th term of the A.P. is 47, then find its nth term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 98
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 99

Question 85.
Find the sum of all multiples of 7 lying between 500 and 900.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 100

Question 86.
Find the sum of all multiples of 8 lying between 201 and 950.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 101

Question 87.
Find the sum of all multiples of 9 lying between 400 and 800.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 102

Question 88.
Find the sum of first 40 positive integers divisible by 6
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 103
Question 89.
If 4 times the fourth term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 104

Long Answer Type Questions [4 Marks]

Question 90.
The sum of the first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 105

Question 91.
Sum of the first 20 terms of an A.P. is – 240, and its first term is 7. Find its 24th term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 106

Question 92.
Sum of the first 14 terms of an A.P. is 1505 and its first term is 10. Find its 25th term.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 107

Question 93.
Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 108

Question 94.
If the sum of the first 7 terms of an A.P. is 119 and that of the first 17 terms is 714, find the sum of its first n-terms. [All India]
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 109

Question 95.
A sum of ? 1600 is to be used to give ten cash prizes to students of a school for their over all academic performance. If each prize is ? 20 less than its preceding prize, find the value of each of the prizes.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 110

Question 96.
The sum of 4th and 8th terms of an A.P. is 24 and the sum of its 6th and 10th terms is 44. Find the sum of first ten terms of the A.P.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 111

Question 97.
The sum of the first five terms of an A.P. is 25 and the sum of-its next five terms is – 75. Find the 10th term of the A.P.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 112
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 113

Question 98.
The sum of the third and seventh terms of an A.P. is 40 and the sum of its sixth and 14th terms is 70. Find the sum of the first ten terms of the A.P.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 114

2011

Short Answer Type Questions I [2 Marks]

Question 99.
Is -150 a term of the AP 17,12, 7, 2,…?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 115

Question 100.
Find the number of two-digit numbers which are divisible by 6.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 116

Question 101.
Which term of the A.P. 3,14,25,36,… will be 99 more than its 25th term
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 117

Question 102.
How many natural numbers are there between 200 and 500, which are divisible by 7?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 118

Question 103.
How many two-digit numbers are divisible by 7?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 119
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 120

Question 104.
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 121
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 122

Short Answer Type Questions II [3 Marks]

Question 105.
Find the value of the middle term of the following AP. -6,-2,2,…, 58
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 123

Question 106.
Determine the AP whose fourth term is 18 and the difference of the ninth term from the fifteenth term is 30.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 124

Question 107.
Find an AP ,whose fourth team is 9 and the sum of its sixth term and thirteenth term is 40.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 125

Question 108.
Find the sum of first-n-terms of an A.P. whose nth term is 5n – 1. hence find the sum of first 20 terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 126

Question 109.
Find the sum of all odd integers between 1 and 100, which are divisible by 3.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 127

Long Answer Type Questions [4 Marks]

Question 110.
If the sum of first 4 terms of an AP is 40 and that of first 14 terms is 280, find the sum of its first n terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 128

Question 111.
Find the sum of the first 30 positive integers divisible by 6.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 129

Question 112.
The first and the last terms of an AP are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 130

Question 113.
How many multiples of 4 lie between 10 and 250? Also find thier sum.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 131

Question 114.
In an AP, if the 6th and 13th terms are 35 and 70 respectively, find the sum of its first 20 terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 132

Question 115.
In an AP, if the sum of its 4th and 10th terms is 40, and the sum of its 8th and 16th terms is 70, then find the sum of its first twenty terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 133

Question 116.
In an A.P., if the sum of 4th and the 8th terms is 70 and its 15th term is 80, then find the sum of its first 25 terms.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 134
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 135

2010

Very Short Answer Type Questions [1 Mark]

Question 117.
If the sum of first p terms of an AP is ap2 + bp, find its common difference.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 136

Question 118.
If the sum of the first q terms of an AP is 2q + 3q2, what is its common difference?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 137

Question 119.
If the sum of first m terms of an AP is 2m2 + 3m, then what is its second term?
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 138

Short Answer Type Questions I [2 Marks]

Question 120.
In an AP, the first term is 2, the last term is 29 and sum of n terms is 155. Find the common difference of the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 139

Question 121.
Find the common difference of an AP whose first term is 4, the last term is 49 and the sum of all its terms is 265.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 140

Question 122.
In an AP, the first term is – 4, the last term is 29 and the sum of all its terms is 150. Find its common difference.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 141

Short Answer Type Questions II [3 Marks]

Question 123.
In an AP, the sum of first ten terms is – 150 and the sum of its next ten terms is – 550. Find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 142.
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 143

Question 124.
In an AP, the sum of first ten terms is – 80 and the sum of its next ten terms is – 280. Find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 144

Question 125.
The sum of the first sixteen terms of an AP is 112 and the sum of its next fourteen terms is 518. Find the AP.
Solution:
Arithmetic Progressions Class 10 Maths CBSE Important Questions with Solutions 145

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