Question

The sum of first $8$ terms of the geometric series $2+6+18+54+...$is

• A. $6506$
• B. $5650$
• C. $6650$
• D. $6560$

Answer 1

The correct option is D

$6560$

Explanation for the correct option:

The given series is $2+6+18+54+...$

The first term, $a=2$

The second term, $ar=6$

Therefore common ratio $r=\frac{6}{2}=3$

We know that the sum of the G.P series $S_n$$=\frac{a\left(r^n-1\right)}{r-1}$

We have to find the sum of first $8$ term .

Therefore $n=8$

$$\begin{gathered} \Rightarrow S_8=\frac{2\left(3^8-1\right)}{3-1} \\ \Rightarrow S_8=3^8-1 \\ \Rightarrow S_8=6561-1 \\ \Rightarrow S_8=6560 \end{gathered}$$

Hence, option option is D is correct.