Mathematics

The key is recognizing that the partial sums tell you about individual terms: $S_1$ is just the first term, while $S_2$ is the first term plus the second. Once you find those two terms, you can calculate the common ratio $r$, which completely determines the sequence. Then you can use the standard formula for the sum of a geometric series to answer any question about it.

The key is recognizing that the partial sums tell you about individual terms: $S_1$ is just the first term, while $S_2$ is the first term plus the second. Once you find those two terms, you can calculate the common ratio $r$, which completely determines the sequence. Then you can use the standard formula for the sum of a geometric series to answer any question about it.