Question

If the fifth term of an AP is 25 and the ninth term is 37, then find the common difference of the AP.

Answer 1

If the first term is a, the common difference is d and the $n^{th}$ term is $a_n$, then,
$a_n=a+(n-1)d$
$\Rightarrow a_5=a+4d$ and
$a_9=a+8d$

Given,
$a+4d=25$ and $a+8d=37$
$a+4d=25$ ...(i)
$a+8d=37$ ...(ii)
Subtracting (i) from (ii), we get
$a+8d-a-4d=37-25$
$⟹4d=12$
$⟹d=3$