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

NCERT Solutions have been carefully compiled and developed as per the latest CBSE syllabus. The NCERT Solutions contain detailed step-by-step explanation of all the problems that are present in the NCERT textbook. The Exercise 9.4 of NCERT Solutions for Class 11 Maths Chapter 9- Sequences and Series is based on the topic Sum to n Terms of Special Series. In this exercise, different types of series are given whose sum to n terms has to be found out.

The NCERT Solutions for Class 11 Maths enhance topics with engaging math activities that strengthen the concepts further. Each question of the exercise has been carefully solved for the students to understand, keeping the examination point of view in mind.

Download PDF of NCERT Solutions for Class 11 Maths Chapter 9- Sequences and Series Exercise 9.4

ncert sol class 11 maths ch 9 ex 4 1
ncert sol class 11 maths ch 9 ex 4 2
ncert sol class 11 maths ch 9 ex 4 3
ncert sol class 11 maths ch 9 ex 4 4
ncert sol class 11 maths ch 9 ex 4 5
ncert sol class 11 maths ch 9 ex 4 6
ncert sol class 11 maths ch 9 ex 4 7

 

Access other exercise solutions of Class 11 Maths Chapter 9- Sequences and Series

Exercise 9.1 Solutions 14 Questions

Exercise 9.2 Solutions 18 Questions

Exercise 9.3 Solutions 32 Questions

Exercise 9.4 Solutions 10 Questions

Miscellaneous Exercise On Chapter 9 Solutions 32 Questions

Access Solutions for Class 11 Maths Chapter 9.4 Exercise

Find the sum to n terms of each of the series in Exercises 1 to 7.

1. 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

Solution:

Given series is 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

It’s seen that,

nth term, an = n ( n + 1)

Then, the sum of n terms of the series can be expressed as

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 1

2. 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

Solution:

Given series is 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

It’s seen that,

nth term, an = n ( n + 1) ( n + 2)

= (n2 + n) (n + 2)

= n+ 3n+ 2n

Then, the sum of n terms of the series can be expressed as

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 2

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 3

3. 3 × 12 + 5 × 22 + 7 × 32 + …

Solution:

Given series is 3 ×12 + 5 × 22 + 7 × 32 + …

It’s seen that,

nth term, an = ( 2n + 1) n2 = 2n3 + n2

Then, the sum of n terms of the series can be expressed as

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 4

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 5

4. Find the sum to n terms of the series 

Solution:

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 6

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

Solution:

Given series is 52 + 62 + 72 + … + 202

It’s seen that,

nth term, an = ( n + 4)2 = n2 + 8n + 16

Then, the sum of n terms of the series can be expressed as

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 7

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 8

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

Solution:

Given series is 3 × 8 + 6 × 11 + 9 × 14 + …

It’s found out that,

a= (nth term of 3, 6, 9 …) × (nth term of 8, 11, 14, …)

= (3n) (3n + 5)

= 9n2 + 15n

Then, the sum of n terms of the series can be expressed as

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 9

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

Solution:

Given series is 12 + (12 + 22) + (12 + 2+ 32 ) + …

Finding the nth term, we have

an = (12 + 22 + 32 +…….+ n2)


NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 10

Now, the sum of n terms of the series can be expressed as

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 11

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

Solution:

Given,

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

Now, the sum of n terms of the series can be expressed as

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 12

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

Solution:

Given,

nth term of the series as:

an = n2 + 2n

Then, the sum of n terms of the series can be expressed as

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 13

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

Solution:

Given,

nth term of the series as:

an = (2n – 1)2 = 4n2 – 4n + 1

Then, the sum of n terms of the series can be expressed as

NCERT Solutions Class 11 Mathematics Chapter 9 ex.9.4 - 14

1 Comment

  1. It is very beneficial for us… Thank you so much 🙏🙏🙏👍👍😊😊

Leave a Comment

Your email address will not be published. Required fields are marked *