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

**Question 1.**

**1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ………**

**Solution:**

In the given series, there is a sum of multiple corresponding terms of two A.P’s. The two A.P’s are

**Question 2.**

**1 x 2 x 3 + 2 x 3 x 4 + 3 x 4 x 5 + ……**

**Solution:**

In the given series, there is a sum of multiple of corresponding terms of two A.P’s. The three A.P’s are

**Question 3.**

**3 x 1 ^{2} + 5 x 2^{2} + 7 x 3^{2} + …..**

**Solution:**

In the given series there is sum of multiple of corresponding terms of two A.P’s. The two A.P’s are

**(i) **3, 5, 7, …………… and

**(ii) **1^{2}, 2^{2}, 3^{2}, ………………….

Now the n^{th} term of sum is an = (nth term of the sequence formed by first A.P.) x (n^{th} term of the sequence formed by second A.P.) = (2 n + 1) x n^{2} = 2n^{3} + n^{2} Hence, the sum to n terms is,

**Question 4.**

…….

**Solution:**

In the given series there is sum of multiple of corresponding terms of two A.P’s. The two A.P’s are

**Question 5.**

**5 ^{2} + 6^{2} + 7^{2} + ………….. + 20^{2}**

**Solution:**

The given series can be written in the following way

**Question 6.**

**3 x 8 + 6 x 11 + 9 x 25 + ………….**

**Solution:**

In the given series, there is sum of multiple of corresponding terms of two A.P/s. The two A.P/s are

**(i) **3, 6, 9, ………….. and

**(ii)** 8, 11, 14, ……………….

Now the nth term of sum is an = (n^{th} term of the sequence formed by first A.P.) x (n^{th} term of the sequence formed by second A.P.)

**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} + …………….. + n^{2}

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

**Question 8.**

**n(n + 1)(n + 4)**

**Solution:**

We have

**Question 9.**

**n ^{2} + 2^{n}**

**Solution:**

We have a_{n} = n^{2} + 2^{n}

Hence, the sum to n terms is,

**Question 10.**

**(2n – 1) ^{2}**

**Solution:**

We have