Question

In an A.P., 7 times the 7th term is equal to 11 times the 11th term. Find the 18th term of the A.P.

Answer 1

WE can see that : $7\times T_7=11\times T_{11}$
$7(a+6d)=11(a+10d)$
$7a+42d=11a+110d7a-11a=110d-42d$
$-4a=68d\therefore a=-17d$
Consider, $T_{18}=a+17d=-17d+17d\therefore T_{18}=0$