**CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.3 Question 8**

**8. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.**

**Solution:**

It is given that second and third term of AP are 14 and 18 respectively.

**Using formula** , to find nth term of arithmetic progression, **we can say that**

** **

**(1)**

And,

** (2)**

These are equations consisting of two variables. We can solve them by the method of substitution.

Using equation **(1),** we can say that

Putting value of in equation **(2), **we can say that

Therefore, common difference

Putting value of in equation number **(1)**, we can say that

**Applying formula**, to find sum of n terms of AP, **we get**

**Therefore, sum of first 51 terms of an AP is equal to 5610.**