Sequences and Series - Solutions

Sequences and Series - Solutions

CBSE Class–11 Mathematics

NCERT Solutions
Chapter - 9 Sequences and Series
Exercise 9.1

Write the first five terms of each of the sequences in Exercises 1 to 6 whose terms are:

1.

Ans. Given:

Putting and 5, we get,

Therefore, the first five terms are 3, 8, 15, 24 and 35.

2.

Ans. Given:

Putting and 5, we get,

Therefore, the first five terms are and

3.

Ans. Given:

Putting and 5, we get,

Therefore, the first five terms are 2, 4, 8, 16 and 32.

4.

Ans. Given:

Putting and 5, we get,

Therefore, the first five terms are and

5.

Ans. Given:

Putting and 5, we get,

$a_{2} = (- 1)^{2 - 1} 5^{2 + 1} = (- 1)^{1} {.5}^{3} = - 1 \times 125 = - 125$

Therefore, the first five terms are and

6.

Ans. Given:

Putting and 5, we get,

Therefore, the first five terms are and

Find the indicated terms in each of the sequences in Exercises 7 to 10 where terms are:

7.

Ans. Given:

Therefore, 17th and 24th terms are 65 and 93 respectively.

8.

Ans. Given:

Therefore, 7th term is

9.

Ans. Given:

Therefore, 9th term is 729.

10.

Ans. Given:

Therefore, 20th term is .

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

11. for all

Ans. Given: for all

Putting and 5, we get

Hence the first five terms are 3,11,35,107,323.

Therefore, corresponding series is 3 + 11 + 35 + 107 + 323 + ……….

12.

Ans. Given:

Putting and 5, we get

Hence the first five terms are $- 1, \frac{- 1}{2}, \frac{- 1}{6}, \frac{- 1}{24}, \frac{- 1}{120}$

Corresponding series is $- 1 + (\frac{- 1}{2}) + (\frac{- 1}{6}) + (\frac{- 1}{24}) + (\frac{- 1}{120}) . . . . . . . . . . . . .$

13.

Ans. Given:

Putting and 5, we get

Hence the first five terms are 2,2,1,0,-1.

Therefore, corresponding series is

14. The Fibonacci sequence is defined by and Find for

Ans. Given: and

Putting 3, 4, 5 and 6, we have

Now,

For

For

For

For

For