Let S_n denote the sum of the first n terms of an A.P.

Question

Let $S_n$ denote the sum of the first $n$ terms of an A.P. If $S_4=16$ and $S_6=-48$, then $S_{10}$ is equal to:

Accepted Answer

$S_4=2(2a+3d)=16 \Rightarrow 2a+3d=8$. $S_6=3(2a+5d)=-48 \Rightarrow 2a+5d=-16$.

Subtracting: $2d=-24 \Rightarrow d=-12$, $a=22$.

$$S_{10} = \frac{10}{2}(44+9(-12)) = -320.$$

Solutions · 1