The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Solution: Here, first term of AP,$a=5$
Last termof AP,$l=45$
Sum of AP, $S=400$
We know,
$S=\frac{n}{2}\left(a+l\right)\Rightarrow 400=\frac{n}{2}\left(45+5\right)\Rightarrow n=8\ast 2=16$
So, number of terms is $16$.
As, last term is $45$, we can write,
$5+\left(16-1\right)d=45$
$d=\frac{40}{15}=\frac{8}{3}$
So, common difference is $\frac{8}{3}$.