Question

If $2,-4,8,-16,..........$ represents a geometric progressions, then find $S_9$.

• A. $342$
• B. $346$
• C. $350$
• D. $354$

Answer 1

The correct option is A $342$

In the given GP,

Second term $=-4=2\times (-2)=-2a$, where $a=2$ is the first term

Third term $=8=2\times (-2{)}^2=(-2{)}^{2}a$

Fourth term $=-16=2\times (-2{)}^3=(-2{)}^{3}a$

Clearly, the given GP has first term $a=2$ and common ratio $r=-2$
$\therefore S_9=a\times \left(\frac{r^9-1}{r-1}\right)=2\times \left(\frac{(-2{)}^9-1}{(-2)-1}\right)$
$=2\times \left(\frac{(-512)-1}{-1-2}\right)$
$=2\times \left(\frac{513}{3}\right)$
$=2\times 171=342$