Question

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

Answer 1

$5\left(5^{th}\right)=8\left(8^{th}\right)$ ${13}^{th}$ term =?

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

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

$-3a=46d$

$a=-12d$

${13}^{th}$ term $=a+\left(12\right)d$

$=-12d+12d=0$