Class 10

Math

All topics

Sequences and Series

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.

Last termof AP,$l=45$

Sum of AP, $S=400$

We know,

$S=2n (a+l)⇒400=2n (45+5)⇒n=8∗2=16$

So, number of terms is $16$.

As, last term is $45$, we can write,

$5+(16−1)d=45$

$d=1540 =38 $

So, common difference is $38 $.