guessing geometric series from a partial sum?

Question

I had thought the answer would be $b$ since the graph seems to be nearing a specific value and the infinite geometric sum is defined only when $|r| < 1$. However, the answer states it is $c$. Am I wrong (if so how and why), or is the answer wrong?

Answer 1

Your answer was almost certainly the intended answer. Answer (c) definitely can't be correct, since the partial sums of a geometric series with $r>1$ would be growing faster and faster, since the powers of $r$ are increasing.

[As pointed out in the comments, the exact graph shown is not actually correctly to scale to be a geometric series, so all of the answers are wrong if you assume it is drawn accurately and not just a very rough sketch. This is probably an error of laziness on the part of whoever wrote the problem: they just drew a graph of roughly the shape they wanted, without checking whether it actually numerically worked.]