Problem
Determine the sum of the first four terms of the geometric sequence where $a=5$ and $r=3$. The sum is $\square$.
Solution
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 \(\boxed{200}\).
