Problem 29 - College Algebra

Question

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

Step-by-Step Solution

Answer

The result is 105.

Step 1: Understand the Sigma Notation

The problem provides a sum in sigma notation, written as \(\sum_{i=1}^{6} 5i\). The 'i=1' underneath the sigma indicates that the first term of the sum is when i = 1, and the '6' above sigma indicates that the last term of the sum is when i = 6.

Step 2: Write out the Sequence

According to the information provided, the sequence can be written out as: \(5*1, 5*2, 5*3, 5*4, 5*5, 5*6\).

Step 3: Calculate each Term of the Sequence

The sequence becomes: 5, 10, 15, 20, 25, 30.

Step 4: Sum up all the Terms

The sum of all the terms in the sequence is: \(5+10+15+20+25+30=105\).