Question

Let $2,6,18,........$ represents a geometric progression, then find $S_7$.

• A. $2186$
• B. $2196$
• C. $2545$
• D. $2457$

Answer 1

Answer: (A)

$2186$

Given sequence $2,6,18,...$ is a GP

Second term $=6=2\times 3=3a$

Third term $=18=2\times 3\times 3=3^{2}a$

Clearly, the given GP has first term $a=2$ and common ratio $r=3$.
$\therefore S_7=a\times \left(\frac{r^7-1}{r-1}\right)=2\times \left(\frac{(3{)}^7-1}{3-1}\right)$
$=2\times \left(\frac{2187-1}{2}\right)$
$=2\times \left(\frac{2186}{2}\right)$
$=2186$