**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:**

**Question 2.**

For what value of k will k + 9,2k -1 and 2k + 7 are the consecutive terms of an A.P.?

**Solution:**

**Question 3.**

For what value ofk will the consecutive terms 2k + 1, 3k + 3 and 5k -1 form an A.P.?

**Solution:**

**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:**

**Question 5.**

How many terms of the A.P. 27,24,21,… should be taken so that their sum is zero?

**Solution:**

**Question 6**.

How many terms of the A.P. 65,60, 55,… be taken so that their sum is zero?

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Question 18.**

The sum of three numbers in A.P. is 12 and sum of their cubes is 288, Find the numbers.

**Solution:**

**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:**

**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:**

**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:**

**Short Answer Type Questions I [2 Marks]**

**Question 22.**

Find the middle term of the AP 6,13,20,…, 216.

**Solution:**

**Question 23.**

Find the middle term of the AP 213,205,197,…, 37.

**Solution:**

**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:**

**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:**

**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:**

**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:**

**Short Answer Type Questions**

**Question 28.**

**Solution:**

**Question 29.**

**Solution:**

**Question 30.**

It Sn, denotes the sum of first n-terms of an AP. Prove that: S12 = 3 (S8 – S4)

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Question 44.**

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

**Solution:**

**Question 45.**

The sum of the first n terms of an A.P. is 3n^{2} + 6n. Find the nth term of this A.P.

**Solution:**

**Question 46.**

The sum of the first n terms of an AP is 5n – n^{2}. Find the nth term of this AP.

**Solution:**

**Question 47.**

The sum of the first n terms of an AP is 4n^{2} + 2n. Find the nth term of this AP.

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

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:**

**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:**

**Question 55.**

If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20-S10)

**Solution:**

**2013**

**Short Answer Type Questions**

**Question 56.**

How many three digit natural numbers are divisible by 7?

**Solution:**

**Question 57.**

Find the number of all three-digit natural numbers which are divisible by 9.

**Solution:**

**Question 58.**

Find the number of three-digit natural numbers which are divisible by 11

**Solution:**

**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:**

**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:**

**Question 61.**

The sum of first n-terms of an AP is 3n^{2} + 4n. Find the 25th term of this AP.

**Solution:**

**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:**

**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:**

**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:**

**Question 65.**

The 8th term of an AP is 31. If its 15th term exceeds its 11th term by 16, find the AP.

**Solution:**

**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:**

**Question 67.**

The 5th term of an AP exceeds its 12th term by 14. If its 7th term is 4, find the AP.

**Solution:**

**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:**

**Question 69.**

The 24th term of an AP is twice its tenth term. Show that its 72nd term is 4times its 15th term.

**Solution:**

**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:**

**Question 71.**

The sum of first m terms of an AP is 4m^{2} – m. If its n. Also, find the 21st term of this AP.

**Solution:**

**Question 72.**

The sum of first q terms of an AP is 63q – 3q^{2}. If its pth term is -60, find the value of p. Also find the 11th term of this AP.

**Solution:**

**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:**

**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:**

**Question 75.**

Find the sum of all three digit natural numbers, which are multiples of 9.

**Solution:**

**Question 76.**

** Find the sum of all three digits natural numbers, which are multiples of 7.**

** Solution:**

**Question 77.**

How many three digit numbers are divisible by 11?

**Solution:**

**Question 78.**

How many three-digit numbers are divisible by 12?

**Solution:**

**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:**

**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:**

**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:**

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:**

**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:**

**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:**

**Question 85.**

Find the sum of all multiples of 7 lying between 500 and 900.

**Solution:**

**Question 86.**

Find the sum of all multiples of 8 lying between 201 and 950.

**Solution:**

**Question 87.**

Find the sum of all multiples of 9 lying between 400 and 800.

**Solution:**

**Question 88.**

Find the sum of first 40 positive integers divisible by 6

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**2011**

**Short Answer Type Questions I [2 Marks]**

**Question 99.**

Is -150 a term of the AP 17,12, 7, 2,…?

**Solution:**

**Question 100.**

Find the number of two-digit numbers which are divisible by 6.

**Solution:**

**Question 101.**

Which term of the A.P. 3,14,25,36,… will be 99 more than its 25th term

**Solution:**

**Question 102.**

How many natural numbers are there between 200 and 500, which are divisible by 7?

**Solution:**

**Question 103.**

How many two-digit numbers are divisible by 7?

**Solution:**

**Question 104.**

**Solution:**

**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:**

**Question 106.**

Determine the AP whose fourth term is 18 and the difference of the ninth term from the fifteenth term is 30.

**Solution:**

**Question 107.**

Find an AP ,whose fourth team is 9 and the sum of its sixth term and thirteenth term is 40.

**Solution:**

**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:**

**Question 109.**

Find the sum of all odd integers between 1 and 100, which are divisible by 3.

**Solution:**

**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:**

**Question 111.**

Find the sum of the first 30 positive integers divisible by 6.

**Solution:**

**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:**

**Question 113.**

How many multiples of 4 lie between 10 and 250? Also find thier sum.

**Solution:**

**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:**

**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:**

**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:**

**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:**

**Question 118.**

If the sum of the first q terms of an AP is 2q + 3q2, what is its common difference?

**Solution:**

**Question 119.**

If the sum of first m terms of an AP is 2m2 + 3m, then what is its second term?

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**