Question

Determine the A.P. whose fifth tern is 19, and different one of the eight term from the thirteenth term is 20.

Answer 1

Let us consider the first term be $a$ and difference be $d$ in the problem

So,

$\begin{array}{c}{a}_5=19and{a}_{13}-a_8=20\\ a_5=a+\left(5-1\right)d=19\\ a+4d=19\\ and\\ a+\left(13-1\right)d-a+\left(8-1\right)d=20\\ a+12d-a+7d=20\\ 5d=20\\ d=4\\ Onputtingin{a}_5\\ a+4\left(4\right)=19\\ a+16=19\\ a=3\end{array}$

Hence, the A.P will be $a,a+d,a+2d,a+3d,.........$

=$3,3+4,3+2\times 4,.........$

implies that

$3,7,11,.......$