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

NCERT Solutions for Class 11 Maths Chapter 9 have been carefully compiled and developed as per the latest update on the term â€“ I CBSE Syllabus 2021-22. These solutions contain detailed step-by-step explanation of all the problems that are present in the Class 11 NCERT Textbook. 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 term â€“ I examination point of view in mind.

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### 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 Ã— 2 + 2 Ã— 3 + 3 Ã— 4 + 4 Ã— 5 + â€¦

Solution:

Given series is 1 Ã— 2 + 2 Ã— 3 + 3 Ã— 4 + 4 Ã— 5 + â€¦

Itâ€™s seen that,

nthÂ term,Â anÂ =Â nÂ (Â nÂ + 1)

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

2. 1 Ã— 2 Ã— 3 + 2 Ã— 3 Ã— 4 + 3 Ã— 4 Ã— 5 + â€¦

Solution:

Given series is 1 Ã— 2 Ã— 3 + 2 Ã— 3 Ã— 4 + 3 Ã— 4 Ã— 5 + â€¦

Itâ€™s seen that,

nthÂ term,Â anÂ =Â nÂ (Â nÂ + 1) (Â nÂ + 2)

= (n2Â +Â n) (nÂ + 2)

=Â n3Â + 3n2Â + 2n

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

3. 3 Ã— 12Â + 5 Ã— 22Â + 7 Ã— 32Â + â€¦

Solution:

Given series is 3 Ã—12Â + 5 Ã— 22Â + 7 Ã— 32Â + â€¦

Itâ€™s seen that,

nthÂ term,Â anÂ = ( 2nÂ + 1)Â n2Â = 2n3Â +Â n2

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

4. Find the sum toÂ nÂ terms of the seriesÂ

Solution:

5. Find the sum toÂ nÂ terms of the seriesÂ 52Â + 62Â + 72Â + â€¦ + 202

Solution:

Given series is 52Â + 62Â + 72Â + â€¦ + 202

Itâ€™s seen that,

nthÂ term,Â anÂ = (Â nÂ + 4)2Â =Â n2Â + 8nÂ + 16

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

6. Find the sum toÂ nÂ terms of the series 3 Ã— 8 + 6 Ã— 11 + 9 Ã— 14 +â€¦

Solution:

Given series is 3 Ã— 8 + 6 Ã— 11 + 9 Ã— 14 + â€¦

Itâ€™s found out that,

anÂ = (nthÂ term of 3, 6, 9 â€¦) Ã— (nthÂ term of 8, 11, 14, â€¦)

= (3n) (3nÂ + 5)

= 9n2Â + 15n

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

7. Find the sum toÂ nÂ terms of the series 12Â + (12Â + 22) + (12Â + 22Â + 32) + â€¦

Solution:

Given series is 12Â + (12Â + 22) + (12Â + 22Â + 32Â ) + â€¦

Finding the nth term, we have

anÂ = (12Â + 22Â + 32Â +â€¦â€¦.+Â n2)

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

8. Find the sum toÂ nÂ terms of the series whoseÂ nthÂ term is given byÂ nÂ (nÂ + 1) (nÂ + 4).

Solution:

Given,

anÂ =Â nÂ (nÂ + 1) (nÂ + 4) =Â n(n2Â + 5nÂ + 4) =Â n3Â + 5n2Â + 4n

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

9. Find the sum toÂ nÂ terms of the series whoseÂ nthÂ terms is given byÂ n2Â + 2n

Solution:

Given,

nth term of the series as:

anÂ = n2Â + 2n

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

10. Find the sum toÂ nÂ terms of the series whoseÂ nthÂ terms is given by (2nÂ â€“ 1)2

Solution:

Given,

nth term of the series as:

anÂ =Â (2nÂ â€“ 1)2Â = 4n2Â â€“ 4nÂ + 1

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