Determine the AP whose $3^{rd}$term is 5 and the $7^{th}$term is 9.

Solution: To determine an $A.P.$, we need starting term $a$ and difference $d$.
Here, we are given,
$a_3=a+2d=5$
$a_7=a+6d=9$
Subtracting above equations, we get,
$6d-2d=4\Rightarrow d=1$
$a+2=5\Rightarrow a=3$.
So, $A.P.$ will be $3,4,5,6,7,8,9,10\dots$.