Question

Which term of the A.P. 8, 14, 20, 26, .... will be 72 more than its ${41}^{st}$ term?

Answer 1

A.P. is 8, 14, 20, 26....
a = 8, d = 14 - 8 = 6
Let $a_n=a_{41}+72$
$\Rightarrow a+(n-1)d=a+40d+72$
$\Rightarrow (n-1)6=40\times 6+72$
$=240+72$
$\Rightarrow n-1=\frac{312}{6}=52$
$\Rightarrow n=52+1={53}^{rd}term$