Question

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

• A. $1842$
• B. $1852$
• C. $1862$
• D. $1872$

Answer 1

The correct option is C $1862$

Let first term of $A.P.$ be a and common difference is $d$.
$\therefore S_{10}=\frac{10}{2}\{2a+9d\}=530$
$\therefore 2a+9d=106\cdots \left(i\right)$
$S_5=\frac{5}{2}\{2a+4d\}=140$
$a+2d=28\cdots \left(ii\right)$
from equation $\left(i\right)$ and $\left(ii\right),a=8,d=10$
$\therefore S_{20}-S_6=\frac{20}{2}\{2\times 8+19\times 10\}-\frac{6}{2}\{2\times 8+5\times 10\}$
$=2060-198=1862$