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

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

NCERT TEXTBOOK EXERCISES

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:

Ex 9.1 Class 11 Maths Question 3.
an = 2n

Solution:

Ex 9.1 Class 11 Maths Question 4.
an = $\frac { 2n-3 }{ 6 }$

Solution:

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

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

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

Ex 9.1 Class 11 Maths Question 9.
an = (-1)n – 1 n3; a9

Solution:

We have, an = (-1)n – 1 n3

Ex 9.1 Class 11 Maths Question 10.
an = $\frac { n(n-2) }{ n+3 }$; a 20

Solution:

We have, an = $\frac { n(n-2) }{ n+3 }$

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

Hence the first five terms of the given sequence are – 1, -1/2, -1/6, -1/24, -1/120.
The corresponding series is

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 Exercise 9.1 PDF

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