Question

$m,2m,4m,...$
The first term in the sequence above is $m$, and each term thereafter is equal to twice the previous term. If $m$ is an integer, which of the following could NOT be the sum of the first four terms of this sequence?

• A. $-26$
• B. $-15$
• C. $45$
• D. $75$
• E. $120$

Answer 1

Answer: (A)

$-26$

The first term in given Geometric series, $a_1=m$
The common ratio $r$ $=\frac{4m}{2m}=2$
No. of terms, $n$ $=4$
Applying sum of GP formula,
$S_n=\frac{a(1-r^n)}{1-r}$
$=\frac{m(1-2^4)}{1-2}$
$=\frac{m(1-16)}{-1}=15m$

If $m$ is an integer the sum of the first four terms of this sequence should be in multiple of $15$.
Hence, option A is correct which is not a multiple of $15$.