If the third and the ninth terms of an AP are 4 and -8 respectively, which term of this AP is zer

To find out which term of this AP is zero, we first need to find the common difference (d) of the AP.

The formula for the nth term of an AP is: a + (n-1)d

Given that the third term (n=3) is 4 and the ninth term (n=9) is -8, we can set up the following equations:

4 = a + 2d (equation 1) -8 = a + 8d (equation 2)

Subtract equation 1 from equation 2 to find d:

-8 - 4 = a + 8d - (a + 2d) -12 = 6d d = -12 / 6 = -2

Substitute d = -2 into equation 1 to find a:

4 = a + 2*(-2) 4 = a - 4 a = 4 + 4 = 8

Now that we have a = 8 and d = -2, we can find out which term of this AP is zero by setting the nth term equal to zero and solving for n:

0 = 8 + (n-1)*(-2) 0 = 8 - 2n + 2 0 = 10 - 2n 2n = 10 n = 10 / 2 = 5

So, the fifth term of this AP is zero.