**Solution:**

Given,

3^{rd} term of the AP is a_{3} = 4

and 9^{th} term, a_{9} = −8

We know that,

a_{n} = a + (n − 1) d

Therefore,

a_{3} = a + (3 − 1) d

4 = a + 2d ….(1)

a_{9} = a + (9 − 1) d

−8 = a + 8d ….(2)

On subtracting equation (1) from (2), we get;

−12 = 6 d

d = −2

From equation (1),

4 = a + 2(−2)

4 = a − 4

a = 8

Let the nth term of this AP be zero.

a_{n } = a + (n − 1) d

0 = 8 + (n − 1)(−2)

0 = 8 − 2n + 2

2n = 10

n = 5

Hence, the 5^{th} term of the AP is 0.