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

Here, a₃ = 4 and a₉ = – 8. To find : n, where a_n = 0
Given that: a₃ = a + (3 – 1)d = 4
⇒ a + 2d = 4
⇒ a = 4 – 2d . . .(1)
and a₉ = – 8
⇒ a + 8d = – 8
Putting the value of a from equation (1), we get
4 – 2d + 8d = -8
⇒ 6d = – 12 ⇒ d = -2
putting the value of d in equation (1), we get
a = 4 – 2(- 2) = 8
putting the values in a_n = 0, we get
a_n = a + (n -1)d = 0
⇒ 8 +(n -1)(- 2) = 0
⇒ n – 1 = 1 = 4 ⇒ n = 5
Hence, the 5th term of this AP is zero.