Question

If the ${10}^{th}$ term of an A.P. is $52$ and the ${17}^{th}$ term is $20$ more than the ${13}^{th}$ term, find the A.P.

Answer 1

Let $a$ be the first term and $d$ be the common difference of the A.P.
We have,
$a_{10}=52$ and $a_{17}=a_{13}+20$

$⟹a+9d=52$ and $a+16d=a+12d+20$

$⟹a+9d=52$ and $4d=20$

$⟹a+9d=52$ and $d=5$

$⟹a+45=52$ and $d=5$

$⟹a=7$ and $d=5$
Hence, the A.P. is $a,a+d,a+2d,a+3d,....$ i.e. $7,12,17,22,....$