Question

If thrice the third term of an A.P, equal to $5$ times its fifth term. Then show that $8$th term is zero.

Answer 1

Let $a$ be the first term and $d$ is the common difference of the A.P.

Then according to the problem,

$3(a+2d)=5(a+4d)$

or, $2a+14d=0$

or, $a+7d$=0$......(1)

Now the eight-th term of the A.P. is $(a+7d)=0$. [ By (1)].