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

Given

a_n = 0, n = ?

3^rd term = 4

⇒ a + (3-1)d = 4 → 1

9^th term = 73

⇒ a + (9-1)d = -8 → 2

By subtracting the both equations we will get ‘d’

(a +2d) – (a+8d) = 4 – (-8)

-6d = 12

d = -2

By substituting “d” in equation 1

a +2d = 4

a + (-2)2 = 4

a = 8

a_n = a+(n-1)d

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

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

4 = n-1

n = 5

∴ 0 is the 5^th term in the series.