Question

If the $5^{th}$ term of an A.P. is $31$ and ${25}^{th}$ term is $140$ more than the $5^{th}$ term, then find the A.P.

Answer 1

General $n^{th}$ term in AP, $a_n=a+(n-1)d$

$a=$ first term, $d=$ common difference.

Given, $a_5=31$

$\Rightarrow a+4d=31$ and $a_{25}=140+a_5$

$\Rightarrow a+24d=140+a+4d$

$\Rightarrow 20d=140$

$\Rightarrow d=7$

$\Rightarrow a=3$

$\Rightarrow A.P=3,10,17,24$,....