Problem 29 - College Algebra

Question

Find each indicated sum. $$\sum_{i=1}^{6} 5 i$$

Step-by-Step Solution

Answer

The indicated sum is 105.

Step 1: Identify the range and function

First, identify the range of the sum; i goes from 1 to 6. The function is 5*i.

Step 2: Evaluate the function for all i

Now, list the results that are obtained when you replace each i from 1 to 6 into the function \(5i = 5*1, 5*2, 5*3, 5*4, 5*5, 5*6\) which gives \(5, 10, 15, 20, 25, 30\).

Step 3: Sum the terms

Next, fine the total value of the sum, \(\sum_{i=1}^{6} 5 i = 5 + 10 + 15 + 20 + 25 + 30 = 105\).