Question

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

Answer 1

Given, $a_{10}=52;a_{17}=a_{13}+20$
$\Rightarrow a+16d=a+12d+20\Rightarrow 16d=12d+20\Rightarrow 4d=20\Rightarrow d=\frac{20}{4}=5$
Also, a + 9d = 52
$\Rightarrow a+9\times 5=52$
a + 45 = 52
a = 7
Therefore A.P. = 7, 12, 17, 22, 27....