Question

In an A.P, $5$ times the $5^{th}$ terms is equal to $8$ times the $8^{th}$ term, then its ${13}^{th}$ terms is

Answer 1

We know that any $a_n$ term of an AP is given by $a_n=a+(n-1)d$

According to the question,

$5a_5=8a_8$

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

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

$\Rightarrow 3a+36d=0$

$\Rightarrow 3(a+12d)=0$

$\therefore a_{13}=0$