Question

The value of $\sum _{n=1}^6(3+2^n)$ is

• A. $144$
• B. $15$
• C. $20$
• D. $100$

Answer 1

The correct option is A $144$

$\sum _{n=1}^6(3+2^n)$
$=3\sum _{n=1}^{6}1+\sum _{n=1}^6{2}^n$
$=3(1+1+\cdots (6\text{times}\left)\right)+(2^1+2^2+\cdots +2^6)$
$=18+\frac{2(2^6-1)}{2-1}$
$=18+126$
$=144$