Question

If the $3^{rd}$ and the $9^{th}$ terms of an arithmetic progession are 4 and -8 respectively, which term of it is zero ?

Answer 1

Given 3rd term =4

ie
a+2d=4................(1)

Also given 9th term =-8

ie
a+ 8d=-8............(2)

subtracting both equations
-6d=12
d=-2
Which gives a=8

let nth term be zero

so
0=a+(n-1)d
-8=(n-1)(-2)
n-1=4
n=5=5th term