Question

Match the following APs with their sums.

• A. 210
• B. 220
• C. 240

Answer 1

The sum of the first $n$ natural numbers is given by
$S_n=\frac{n(n+1)}{2}.$

$1+2+3+4+.....+20=S_{20}$

$=\frac{20(20+1)}{2}$

$=\frac{20\times 21}{2}$

$=210$

$4+8+...+40=4(1+2+...+10)$
$=4\times S_{10}$

$=4\times \frac{10\times 11}{2}$

$=220.$

$2+4+...+30=2(1+2+...+15)$

$=2\times S_{15}$

$=2\times \frac{15\times 16}{2}$

$=240.$