**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, …

n^{th} term of the given
series, a_{n} = n (n + 1) (n + 2)

= (n^{2} + n) (n + 2) = n^{3} +
3n^{2} + 2n

**Ex 9.4 Class 11 Maths Question 3.**

3 × 1^{2}+ 5 × 2

^{2}+ 7 × 3

^{2}+ …..

**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) 1^{2}, 2^{2}, 3^{2}, ……………

Now, the n^{th} term of the given series = (nth term of the first
series) × (n^{th} term of the second series) = (2n + 1) × n^{2} =
2n^{3} + n^{2}

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 n^{th} term of the given series = (nth term
of the first series) × (n^{th} term of the second series)

**Ex 9.4 Class 11 Maths Question 5.**

5^{2}+ 6

^{2}+ 7

^{2}+ ………….. + 20

^{2}

**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 n^{th} term of the series = (n^{th} term of the
sequence formed by first A.P.) × (n^{th} term
of the sequence formed by second A.P.)

**Ex 9.4 Class 11 Maths Question 7.**

1^{2}+ (1

^{2}+ 2

^{2}) + (1

^{2}+ 2

^{2}+ 3

^{2}) + ………….

**Solution:**

In the given series,

a_{n} = 1^{2} + 2^{2} + 3^{2} + ……………..
+ n^{2}

**Find the sum to n terms of the series in Exercises 8 to 10 whose n ^{th} 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.**

n^{2} + 2^{n}

**Solution:**

We have given that, a_{n} = n^{2} + 2^{n}

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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