If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP iszero?

Given, a₃ = 4 and a₉ = - 8

a₃ = a + 2d = 4

a₉ = a + 8d = - 8

Subtracting 3rd term from 9th term, we get;

a + 8d – a – 2d = - 8 – 4 = - 12

6d = - 12

d = - 2

Substituting the value of d in 3rd term, we get;

a + 2(-2) = 4

a – 4 = 4

a = 8

Now; 0 = a + (n – 1)d

0 = 8 + (n – 1)(- 2)

(n – 1)(- 2) = - 8

n – 1 = 4

n = 5

Thus, 5th term of this AP is zero.