Class 11 Maths NCERT Solutions for Chapter 9 Sequences and Series Exercise 9.4

1. Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

Solution

The given series is 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …
n^th term, a_n = n ( n + 1)

2. Find the sum to n terms of the series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

Solution

The given series is 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …
n^th term, a_n = n ( n + 1) ( n + 2)
= (n² + n) (n + 2)
= n³+ 3n²+ 2n

3. Find the sum to n terms of the series 3 × 1² + 5 × 2² + 7 × 3² + …

Solution

The given series is 3 ×1² + 5 × 2² + 7 × 3² + …
n^th term, a_n = ( 2n + 1) n² = 2n³ + n²

4. Find the sum to n terms of the series 1/(1× 2) + 1/(2× 3) + 1/(3× 4) + .....

Solution

5. Find the sum to n terms of the series 5² + 6² + 7² + ... + 20² .

Solution

The given series s 5² + 6² + 7² + .... + 20²
n^th term, a_n = ( n + 4)² = n² + 8n + 16

= 1496 + 1088 + 256
= 2840
∴ 5² + 6² + 7² + ... + 20² = 2840

6. Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…

Solution

The given series is 3 × 8 + 6 × 11 + 9 × 14 + …

a_n= (n^th term of 3, 6, 9 …) × (n^th term of 8, 11, 14, …)

= (3n) (3n + 5)

= 9n² + 15n

7. Find the sum to n terms of the series 1² + (1² + 2²) + (1² + 2² + 3²) + …

Solution

The given series is 1² + (1² + 2²) + (1² + 2²+ 3² ) + …
a_n = (1² + 2² + 3² +….+ n²)

8. Find the sum to n terms of the series whose n^th term is given by n (n + 1) (n + 4).

Solution

a_n = n (n + 1) (n + 4) = n(n²+ 5n + 4) = n³ + 5n² + 4n

9. Find the sum to n terms of the series whose n^th terms is given by n² + 2ⁿ.

Solution

a_n = n² + 2ⁿ

The above series 2, 2², 2³, .... is a G.P. with both the first term and common ratio equal to 2.

10. Find the sum to n terms of the series whose n^th terms is given by (2n – 1)² .

Solution

a_n = (2n – 1)² = 4n² – 4n + 1

NCERT Solutions For Class 11 Maths Chapter 9 Sequences and Series Exercise 9.4