Question

The 8th term of AP is zero . Prove that 38th term is triple of 18th term.

Answer 1

$T_8=a+7d=0$

$\Rightarrow a=-7d$

$T_{38}=a+37d$

$=-7d+37d$

$=30d$

$T_{18}=a+17d$

$=-7d+17d$

$=10d$.

Clearly $T_{38}=3\left(T_{18}\right)$.