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홈 / 라이브러리 / Gaokao essentials: original practice / AI 플래시카드

What is the formula for the sum of the first $n$ terms of a geometric sequence with first term $a_1$ and common ratio $r \neq 1$?

덱 'Gaokao essentials: original practice'의 플래시카드.

정답

$S_n = \frac{a_1(1 - r^n)}{1 - r}$.

해설

Multiplying $S_n$ by $r$ and subtracting $r S_n$ from $S_n$ cancels intermediate terms, yielding $S_n(1 - r) = a_1(1 - r^n)$.

AI 생성 콘텐츠 · 감수: Ada