Problem

Find the sum of the first 10 terms of the geometric sequence with first term 3 and common ratio 2.

Answer

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Answer

Simplify the right side of the equation to get the sum of the first 10 terms.

Steps

Step 1 ：The sum of the first \(n\) terms of a geometric sequence can be found using the formula \(S_n = a \frac{r^n - 1}{r - 1}\) where \(a\) is the first term, \(r\) is the common ratio and \(n\) is the number of terms.

Step 2 ：Substituting \(a = 3\), \(r = 2\) and \(n = 10\) into the formula, we get \(S_{10} = 3 \frac{2^{10} - 1}{2 - 1}\)

Step 3 ：Simplify the right side of the equation to get the sum of the first 10 terms.

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