Determine the sum of the first four terms of the geometric sequence where $a=5$ and $r=3$.

The sum is $\square$.

Answer

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Answer

The sum of the first four terms of the geometric sequence is $\boxed{200}$.

Steps

Step 1 ：Determine the sum of the first four terms of the geometric sequence where $a=5$ and $r=3$.

Step 2 ：Use the formula for the sum of the first $n$ terms of a geometric sequence: $S_n = a \cdot \frac{1 - r^n}{1 - r}$.

Step 3 ：Substitute $a = 5$, $r = 3$, and $n = 4$ into the formula: $S_n = 5 \cdot \frac{1 - 3^4}{1 - 3}$.

Step 4 ：Simplify the expression to find that $S_n = 200.0$.

Step 5 ：The sum of the first four terms of the geometric sequence is $\boxed{200}$.