Question

$x,2x,4x,...$
The first term in the sequence above is $x$, and each term thereafter is equal to twice the previous term. Find the sum of the first five terms of this sequence.

• A. $10x$
• B. $15x$
• C. $30x$
• D. $31x$
• E. $32x$

Answer 1

The correct option is D $31x$

The first term in given GP, $a_1=x$

The common ratio $r$ $=\frac{4x}{2x}=2$
No. of terms, $n$ $=5$
Applying sum of GP formula,
$S_n=\frac{a(r^n-1)}{r-1}$
$=\frac{x\left(\right(2^5)-1)}{2-1}$
$=\frac{x(32-1)}{1}=31x$
Hence, option D is correct.