# If the 3^{rd} and the 9^{th} terms of an AP are 4 and - 8 respectively, which term of this AP is zero?

**Solution:**

The formula for n^{th} term of an AP is a_{n} = a + (n - 1) d

Here, a_{n} is the n^{th} term, a is the first term, d is the common difference and n is the number of terms.

Third term of the AP = 4

a_{n} = a + (3 - 1)d = 4

a + 2d = 4 .... (1)

9^{th} term of AP = - 8

a_{n} = a + (9 - 1)d = 4

a + 8d = - 8 ....(2)

Solving (1) and (2) for a and d

a + 2d = 4

a + 8d = - 8

- 6d = 12

d = - 2

Putting d = - 2 in equation (1)

a + 2 × ( - 2) = 4

a - 4 = 4

a = 8

Now, by using the values of a and d, we will find the number of terms.

a + (n - 1)d = 0

8 + (n - 1)(- 2) = 0

n - 1 = 4

n = 5

Answer: 5^{th} term will be 0.

**Video Solution:**

## If the 3^{rd} and the 9^{th} terms of an AP are 4 and - 8 respectively, which term of this AP is zero?

### NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 9 - Chapter 5 Exercise 5.2 Question 9:

IIf the 3^{rd} and the 9^{th} terms of an AP are 4 and - 8 respectively, which term of this AP is zero?

0 is the 5th term of the AP in which the 3rd and the 9th terms are 4 and -8 respectively