Solution:

Provided that,

a₃ = 4 is the 3^rd term

and, a₉ = −8 is the 9^th term

We all know that,

a_n = a+(n−1)d

Therefore,

a₃ = a+(3−1)d

4 = a+2d ……………………………………… (i)

a₉ = a+(9−1)d

−8 = a+8d ………………………………………………… (ii)

 (ii) – (i), we get,

−12 = 6d

d = −2

From the equation (i), we get,

4 = a+2(−2)

4 = a−4

a = 8

Let n^th term of this A.P. be zero.

a_n = a+(n−1)d

0 = 8+(n−1)(−2)

0 = 8−2n+2

2n = 10

n = 5 As a result, 5^th term of the above A.P. is 0.