Let S_n denote the sum of the first n terms of an arithmetic progression.

Question

Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10}=530$, $S_5=140$, then $S_{20}-S_6$ is equal to:

Accepted Answer

$S_n=An^2+Bn$: $100A+10B=530$, $25A+5B=140$. Solving: $A=5$, $B=3$.

$$S_{20}-S_6 = 5(400-36)+3(20-6) = 5(364)+3(14) = 1820+42 = 1862.$$

Solutions · 1