Problem 37 - College Algebra

Question

Find each indicated sum. $$\sum_{i=5}^{9} 11$$

Step-by-Step Solution

Answer

The sum from the 5th term to the 9th term inclusive of a constant series where each term is 11 is 55.

Step 1: Find the Number of Terms

To find the number of terms in the series, working out \(i_{final} - i_{initial} + 1\). In this case, \(i_{final}\) is 9 and \(i_{initial}\) is 5, thus the number of terms \(n = 9 - 5 + 1 = 5\).

Step 2: Calculate the Sum

Each term in the series is 11 so multiplying that by the number of terms (which is 5) gives us the total sum. So the sum \(\sigma = n \cdot t = 5 \cdot 11 = 55\).