Question

In a certain A.P. $5$ times the $5$th term is equal to $8$ times the $8$th term, then find its $13$th term.

Answer 1

Given: In an A.P

$\Rightarrow 5\times t_5=8\times t_8$

$\Rightarrow 5(a+4d)=8(a+7d)$

$\Rightarrow 5a+20d=8a+56d$

$\Rightarrow 8a-5a=20d-56d$

$\Rightarrow 3a=-36d$

$\Rightarrow a=\frac{-36d}{3}=-12d$

To find:$t_{13}=a+12d=-12d+12d=0$ since $a=-12d$

$\therefore {13}^{th}$ term is $0$