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

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

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

NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.4 are the part of NCERT Solutions for Class 11 Maths. Here you can find the NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series Ex 9.4.

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

### Ex 9.4 Class 11 Maths Question 1.

1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ………

Solution:
In the given series, there is a sum of the product of corresponding terms of two AP’s. The two AP’s are

### Ex 9.4 Class 11 Maths Question 2.

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

Solution:
In the given series, there is a sum of the product of corresponding terms of three AP’s. The three AP’s are:

1, 2, 3, 4, …

2, 3, 4, 5, …

3, 4, 5, 6, …
nth term of the given series, an = n (n + 1) (n + 2)
= (n2 + n) (n + 2) = n3 + 3n2 + 2n

### Ex 9.4 Class 11 Maths Question 3.

3 × 12 + 5 × 22 + 7 × 32 + …..

Solution:
In the given series, there is a sum of the product of corresponding terms of two series. The two series are:
(i) 3, 5, 7, …………… and
(ii) 12, 22, 32, ……………
Now, the nth term of the given series = (nth term of the first series) × (nth term of the second series) = (2n + 1) × n2 = 2n3 + n2

Hence, the sum to n terms is,

### Ex 9.4 Class 11 Maths Question 4.

Solution:
In the given series, there is a sum of the product of corresponding terms of two series. The two series are:

1/1, ½, 1/3, …. and

½, 1/3, 1/4, ….

Now, the nth term of the given series = (nth term of the first series) × (nth term of the second series)

### Ex 9.4 Class 11 Maths Question 5.

52 + 62 + 72 + ………….. + 202

Solution:
The given series can be written in the following way

### Ex 9.4 Class 11 Maths Question 6.

3 × 8 + 6 × 11 + 9 × 14 + ………….

Solution:
In the given series, there is a sum of the product of corresponding terms of two AP’s. The two AP’s are:
(i) 3, 6, 9, ………….. and
(ii) 8, 11, 14, ……………….
Now, the nth term of the series = (nth term of the sequence formed by first A.P.) ×  (nth term of the sequence formed by second A.P.)

### Ex 9.4 Class 11 Maths Question 7.

12 + (12 + 22) + (12 + 22 + 32) + ………….

Solution:
In the given series,
an = 12 + 22 + 32 + …………….. + n2

Find the sum to n terms of the series in Exercises 8 to 10 whose nth terms is given by:

### Ex 9.4 Class 11 Maths Question 8.

n(n + 1)(n + 4)

Solution:
We have given that,

### Ex 9.4 Class 11 Maths Question 9.

n2 + 2n

Solution:
We have given that, an = n2 + 2n
Hence, the sum to n terms is,

### Ex 9.4 Class 11 Maths Question 10.

(2n – 1)2

Solution:
We have given that,

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