$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?

The sum of the first four terms of this geometric progression is $m + 2m + 4m + 8m = 15m$. Since $m$ must be an integer, the sum of the first four terms must be a direct multiple of 15. Testing the given options by dividing them by 15 shows that $-15$, $45$, and $75$ yield integer results, but $-26$ does not yield an integer, making it an impossible sum.

• Thanks
• Wrong explanation