Problem 38 - College Algebra

Question

Find each indicated sum. $$\sum_{i=3}^{7} 12$$

Step-by-Step Solution

Answer

The sum of the series is 60.

Step 1: Calculate Number Of Terms

The first step is to calculate the number of terms in the series. This is simply obtained by subtracting the lower limit of the series from the upper limit and adding 1 to the result. That is, \(n = 7 - 3 + 1 = 5\). Hence, there are 5 terms in the series.

Step 2: Multiply terms count by Constant

The next step is to multiply the number of terms by the constant. So we get \(\sum_{i=3}^{7} 12 = n \times 12 = 5 \times 12 = 60. \) Hence, the sum of the series is 60.