Question

If the sum of first 4 terms of an AP is 40 and that of first 14 terms is 280 . Find the sum of its n terms

Answer 1

Given- Sum of first 4 terms of an AP is 40 and first 14 term is 280.

$\because S_n=$ sum of n terms of an A.P. $=\frac{n}{2}[2a+(n-1\left)d\right]$

$\Rightarrow S₄=40=\frac{4}{2}[2a+3d]=2a+3d=20...........\left(1\right)$

and

$S₁₄=280=\frac{14}{2}[2a+13d]=2a+13d=40.........\left(2\right)$

solving (1) and (2)

Gives $a=7$ and $d=2$

So $S_n=\frac{n}{2}\left[2\right(7)+(n-1\left)2\right]=7n+n²-n=n²+6n$