Summation Notation

Find the value of the following summation:

Step 1. Determine if the sequence is arithmetic or geometric.

The function representing the sequence is linear. Therefore, the summation represents an arithmetic series.

Step 2. Determine a₁and a_n. For this example, the first term is a₁₅and the last term is a₂₇.

and

Step 3. Determine the number of pairs.

For this example, n = 15 is the first term and n = 27 is the last term. This means there are 13 terms in this series.

Step 4. To find the series, substitute and solve.