Question
For a geometric sequence with first term $a_{1}$ and common ratio $r,$ where $r \neq 0, r \neq 1,$ the sum of the first $n$ terms is $S_{n}=a_{1} \cdot \frac{1-r^{n}}{1-r}$
Step 1
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio is denoted as $r$. Show more…
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Key Concepts
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The sum of $n$ terms of a geometric sequence: $a_{1}+a_{1} r+a_{1} r^{2}+\cdots+a_{1} r^{n-1}=\frac{a_{1}-a_{1} r^{n}}{1-r}$
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