Question

If the 3rd and the 9th terms of an arithmetic progression are 4 and minus 8 respectively, which term of it is zero

Answer 1

Let the first term and common difference be a and d respectively
Ao a3=4
a+2d=4--------------------(1)
a9=-8
a+8d=-8--------------------(2)
Eq(1)-eq(2)
-6d=12
d=-2
Put d in eq 1
a-4=4
a=8
Now let nth term be zero
So an =0
a +(n-1)d=0
8+(n-1)(-2)=0
n-1=4
n=5th term

Answer 2

First lets consider if the 3rd term is 4 and the 9th term is -8, then we can write it as

a+(3–1)d=4 and a+(9–1)d=-8

on solving these equations we get that a=8 and d= -2

Now, we can equate the general form of an a.p. term to zero and find the respective n i.e. 8+(n-1)*(-2)=0

on solving this we get, n=5

Hence zero is the fifth term of the a.p.