Class 11

Math

Co-ordinate Geometry

Straight Lines

$m,2m,4m,...$

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?

- $−26$
- $−15$
- $45$
- $75$
- $120$

The common ratio $r$ $=2m4m =2$

No. of terms, $n$ $=4$

Applying sum of GP formula,

$S_{n}=1−ra(1−r_{n}) $

$=1−2m(1−2_{4}) $

$=−1m(1−16) =15m$

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 $15$.

Hence, option A is correct which is not a multiple of $15$.