Question

The first term of an A.P. is $-7$ and the common difference $5$. Find its ${18}^{th}$ term and the general term.

Answer 1

We have,

$a=$ First term $=-7$ and, $d=$ Common difference $=5$

$a_{18}=a+(18-1)d$ $[\because a_n=a+(n-1\left)d\right]$

$⟹a_{18}=a+17d=-7+17\times 5=78$

and the general term $a_n=a+(n-1)\times 5=-7+(n-1)\times 5$

$⟹a_n=-7+5n-5=5n-12$