In Exercises 61–68, use the graphs of and to find each indicated sum.∑i=15(2ai+bi)\sum_{i=1}^5(2a_{i}+b_{i})

Ch. 8 - Sequences, Induction, and Probability

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Blitzer 8th Edition

Ch. 8 - Sequences, Induction, and Probability

문제 63

9장, 문제 63

In Exercises 61–68, use the graphs of and to find each indicated sum.

$\sum_{i = 1}^{5} (2 a_{i} + b_{i})$

검증된 단계별 안내

Identify the values of the sequences $a_n$ and $b_n$ for $n = 1, 2, 3, 4, 5$ from the graphs. For $a_n$, read the y-values of the red points at these $n$-values. For $b_n$, do the same.

Write down the values explicitly: $a_1, a_2, a_3, a_4, a_5$ and $b_1, b_2, b_3, b_4, b_5$.

Form the expression inside the summation for each $i$ from 1 to 5: calculate $2a_i + b_i$ for each $i$.

Sum all the values obtained in the previous step: $\sum_{i=1}^5 (2a_i + b_i) = (2a_1 + b_1) + (2a_2 + b_2) + (2a_3 + b_3) + (2a_4 + b_4) + (2a_5 + b_5)$.

This sum will give the final result for the indicated sum. You can now substitute the values and perform the arithmetic to find the answer.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Sequences and Terms

A sequence is an ordered list of numbers where each number is called a term. The term a_n represents the value of the sequence at position n. Understanding how to read and interpret terms from a graph is essential for evaluating sums involving sequences.

Summation Notation

Summation notation (∑) is a concise way to represent the sum of a sequence of terms. The index i runs from the lower limit to the upper limit, and the expression inside the summation is evaluated for each i and then added together. This notation is key to solving problems involving sums of sequences.

Combining Sequences in Sums

When summing expressions involving multiple sequences, such as 2a_i + b_i, each term from the sequences must be evaluated at the same index i, multiplied or added as indicated, and then summed over the specified range. This requires careful substitution and arithmetic using the values from the graphs.

In Exercises 61–68, use the graphs of and to find each indicated sum.∑i=15(2ai+bi)\(\sum\)_{i=1}^5(2a_{i}+b_{i})