Question

If five times the fifth term of an A.P. is equal to 8 times its eighth term, show that its ${13}^{th}$ term is zero.

Answer 1

Let $a_1$, $a_2$, $a_3$..... $a_n$.... be the A.P. with its first term = a and common difference = d.

It is given that

5$a_5$ = 8$a_8$

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

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

$\Rightarrow 3a+36d=0$

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

$\Rightarrow a+12d=0$

$\Rightarrow a+(13–1)d=0$

$\Rightarrow a_{13}=0$