In Exercises 61–68, use the graphs of and to find each indicated sum.
5Σi=4 (a_i/b_i)^3
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sequences
A sequence is an ordered list of numbers, typically defined by a specific rule or formula. In this context, sequences a_n and b_n represent two distinct sets of values plotted on a graph, where each term corresponds to a specific index n. Understanding how to interpret these sequences is crucial for performing operations like summation.
Summation notation, represented by the sigma symbol (Σ), is a concise way to express the sum of a sequence of terms. In the given question, the notation 5Σi=4 indicates that we are summing the values of a specific expression from i=4 to 5. Mastery of this notation is essential for calculating the total of the specified terms in the sequences.
A rational function is a ratio of two polynomial functions. In this case, the expression (a_i/b_i)^3 involves dividing the terms of sequence a_n by those of sequence b_n and then cubing the result. Understanding how to manipulate and evaluate rational functions is key to solving the problem effectively.