**CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.2 Question 9**

**9. If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zero?**

**Solution:**

It is given that 3rd and ninth term of AP are 4 and -8 respectively.

It means and where, and are third and ninth terms respectively.

**Using formula** , **to find** nth term of arithmetic progression, we get

4 = a + (3-1)d And, -8 = a + (9-1)d

And,

These are equations in two variables. Lets solve them using method of substitution.

Using equation , we can say that .

Putting value of in other equation , we get

Putting value of in equation , we get

Therefore, first term and Common Difference

We want to know which term is equal to zero.

**Using formula** , **to find** nth term of arithmetic progression, **we get**

**Therefore, 5th term is equal to .**