Question

If the seventh term of an AP is $13$ and its ninth term is $17$, find its 3rd term.

Answer 1

Let the first term of AP be $a$

$7th$ term is considered as $a+6d=13\cdots \left(1\right)$

$9th$ term is Considered as $a+8d=17\cdots \left(2\right)$

$\left(2\right)-\left(1\right)2d=4d=2$

Put it in $\left(1\right)$

$a+6\left(2\right)=13a=1$

$3rd$ term is $a+2d=1+2\left(2\right)=5$