Question

If $7$ times the $7^{th}$ term of an A.P is equal to $11$ times its ${11}^{th}$ terms, then find its $18th$ term.

Answer 1

General term of A.P $\Rightarrow a_n=a+(n-1)d$

$\Rightarrow$ 7 times $7^{th}$ term = 11 times ${11}^{th}$ term

$\Rightarrow 7(a+6d)=11(a+10d)$

$\Rightarrow 7a+42d=11a+110d$

$\Rightarrow$$42-110d=11a-7a$

$\Rightarrow$$-68d=4a$

$\Rightarrow$$-17d=a$ ___ (1)

$\therefore {18}^{th}$ term = $a+17d$

$=-17d+17d$ (from (1))

$=0$

$\therefore {18}^{th}$ term is $0$