Answer
$S_n = \frac{a_1(1 - r^n)}{1 - r}$.
Explanation
Multiplying $S_n$ by $r$ and subtracting $r S_n$ from $S_n$ cancels intermediate terms, yielding $S_n(1 - r) = a_1(1 - r^n)$.
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What is the formula for the sum of the first $n$ terms of a geometric sequence with first term $a_1$ and common ratio $r \neq 1$?
Study flashcard from the deck Gaokao essentials: original practice.