In Exercises 61–68, use the graphs of and to find each indicated sum.
5Σi=1 (a_i^2+1)

Key Concepts

Summation Notation

Summation notation is a mathematical shorthand used to represent the sum of a sequence of terms. It is typically denoted by the Greek letter sigma (Σ), followed by an expression that defines the terms to be summed. In this case, the notation 5Σi=1 indicates that we are summing the expression from i=1 to i=5, which involves evaluating the terms based on the given sequence.

Sequences and Series

A sequence is an ordered list of numbers, where each number is called a term. In this context, the sequence is represented by the points on the graph, with 'n' as the index and 'a_n' as the corresponding term value. A series is the sum of the terms of a sequence, and understanding how to extract and manipulate these terms is crucial for solving the problem.

Function Evaluation

Function evaluation involves substituting specific input values into a function to obtain corresponding output values. In this case, we need to evaluate the function a_i for i=1 to 5, which requires identifying the values of a_n from the graph. This step is essential for calculating the sum of the squares of these values plus one, as indicated in the summation expression.