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NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1.

  • Sequences and Series Class 11 Ex 9.2
  • Sequences and Series Class 11 Ex 9.3
  • Sequences and Series Class 11 Ex 9.4
Board CBSE
Textbook NCERT
Class Class 11
Subject Maths
Chapter Chapter 9
Chapter Name Sequences and Series
Exercise  Ex 9.1
Number of Questions Solved 14
Category NCERT Solutions

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1

Ex 9.1 Class 11 Maths Question 1.
an = n(n + 2)
Solution:
We haven an = n(n + 2)
subtituting n = 1, 2, 3, 4, 5, we get
a1 = 9(1 + 2) = 1 x 3 = 3
a2 = 2(2 + ) = 2 x 4 = 8
a3 = 3(3 + 2) = 3 x 5 = 15
a4 = 4(4 + 2) = 4 x 6 = 24
a5 = 5(5 + 2) = 5 x 7 = 35
∴ The first five terms are 3, 8, 15, 24, 35.

Ex 9.1 Class 11 Maths Question 2.
an = \(\frac { n }{ n+1 } \)
Solution:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 1

Ex 9.1 Class 11 Maths Question 3.
an = 2n
Solution:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 2

Ex 9.1 Class 11 Maths Question 4.
an = \(\frac { 2n-3 }{ 6 } \)
Solution:
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 3
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 4

Ex 9.1 Class 11 Maths Question 5.
an = (- 1)n-1 5n+1
Solution:
We have, an = (- 1)n-1 5n+1
Substituting n = 1, 2, 3, 4, 5, we get
a1 =(-1)1-1 51+1 = (-1)° 52 = 25
a2 =(-1)2-1 52+1 = (-1)1 53 = 125
a3 =(-1)3-1 53+1 = (-1)2 54 = 625
a4 =(-1)4-1 54+1 = (-1)3 55 = -3125
a5 =(-1)5-1 55+1 = (-1)4 56 = 15625
∴ The first five terms are 25, – 125, 625, -3125, 15625.

Ex 9.1 Class 11 Maths Question 6.
an = n\(\frac { { n }^{ 2 }+5 }{ 4 } \)
Solution:
Substituting n = 1, 2, 3, 4, 5, we get
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 6
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 5
Find the indicated terms in each of the sequences in Exercises 7 to 10 whose nth terms are:

Ex 9.1 Class 11 Maths Question 7.
an = 4n – 3; a17, a24
Solution:
We have an = 4n – 3
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 7

Ex 9.1 Class 11 Maths Question 8.
an = \(\frac { { n }^{ 2 } }{ { 2 }^{ n } } \); a7
Solution:
We have, an = \(\frac { { n }^{ 2 } }{ { 2 }^{ n } } \); a7
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 8

Ex 9.1 Class 11 Maths Question 9.
an = (-1)n – 1 n3; a9
Solution:
We have, an = (-1)n – 1 n3
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 9

Ex 9.1 Class 11 Maths Question 10.
an = \(\frac { n(n-2) }{ n+3 } \); a 20
Solution:
We have, an = \(\frac { n(n-2) }{ n+3 } \)
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 10

Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:

Ex 9.1 Class 11 Maths Question 11.
a1 = 3, an = 3an-1+2 for all n>1
Solution:
We have given a1 = 3, an = 3an-1+2
⇒ a1 = 3, a2 = 3a1 + 2 = 3.3 + 2 = 9 + 2 = 11,
a3 = 3a2 + 2 = 3.11 + 2 = 33 + 2 = 35,
a4 = 3a3 + 2 = 3.35 + 2 = 105 + 2 = 107,
a5 = 3a4 + 2 = 3.107 + 2 = 321 + 2 = 323,
Hence, the first five terms of the sequence are 3, 11, 35, 107, 323.
The corresponding series is 3 + 11 + 35 + 107 + 323 + ………..

Ex 9.1 Class 11 Maths Question 12.
a1 = -1, an = \(\frac { { a }_{ n }-1 }{ n } \), n ≥ 2
Solution:
We have given
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 11
Hence the first five terms of the given sequence are – 1, -1/2, -1/6, -1/24, -1/120.
The corresponding series is
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 12

Ex 9.1 Class 11 Maths Question 13.
a1 = a2 = 2, an = an-1 – 1, n >2
Solution:
We have given a1 = a2 = 2, an = an-1 – 1, n >2
a1 = 2, a2 = 2, a3= a2 – 1 = 2 – 1 = 1,
a4 = a3 – 1 = 1 – 1 = 0 and a5 = a4 – 1 = 0 – 1 = -1
Hence the first five terms of the sequence are 2, 2, 1, 0, -1
The corresponding series is
2 + 2 + 1 + 0 + (-1) + ……

Ex 9.1 Class 11 Maths Question 14.
Find Fibonacci sequence is defined by 1 = a1 = a2 and an = an-1 + an-2, n > 2
Find \(\frac { { a }_{ n }+1 }{ { a }_{ n } } \), for n = 1, 2, 3, 4, 5
Solution:
We have,
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.1 13

 

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