Question

For what value of $n$ the $n^{th}$ term of the following two $A.P.s$ are equal ?
$20,25,30,35,..$ and $-17,-10,-3,4,..$

Answer 1

In first A.P $a=2$ $d=5$

$\begin{array}{c}{n}^{th}term=20+\left(n-1\right)5\\ =20+5n-5\\ =5n+15\end{array}$

In second A.P $a=-17$ $d=7$

$\begin{array}{c}{n}^{th}term=-17=\left(n-1\right)7\\ =-17+7n-1\\ =7n-24\end{array}$

$\begin{array}{c}\therefore 7n-24=5n+15\\ 7n-5n=15+24\\ 2n=39\\ n=18\end{array}$