In Exercises 61–68, use the graphs of and to find each indicated sum.∑i=15(ai+3bi)\sum_{i=1}^5(a_{i}+3b_{i})

Ch. 8 - Sequences, Induction, and Probability

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Blitzer 8th Edition

Ch. 8 - Sequences, Induction, and Probability

문제 64

9장, 문제 64

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

$\sum_{i = 1}^{5} (a_{i} + 3 b_{i})$

검증된 단계별 안내

Step 1: 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 points at $n=1, 2, 3, 4, 5$. For $b_n$, do the same for the corresponding $n$ values.

Step 2: Write down the values explicitly. For example, $a_1 = \text{value from graph}$, $a_2 = \text{value from graph}$, and so on, similarly for $b_1, b_2, b_3, b_4, b_5$.

Step 3: Calculate each term inside the summation $a_i + 3b_i$ for $i = 1, 2, 3, 4, 5$. This means multiply each $b_i$ by 3 and then add the corresponding $a_i$.

Step 4: Sum all the calculated terms from Step 3 to find $\sum_{i=1}^5 (a_i + 3b_i)$. This involves adding the five values obtained for each $i$.

Step 5: Write the final expression for the sum, showing the addition of all terms explicitly, but do not compute the numerical total as per instructions.

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 nth term of sequence a, and similarly b_n for sequence b. Understanding how to identify and interpret terms from graphs is essential for working with sequences.

Summation Notation (Sigma Notation)

Summation notation, represented by the Greek letter sigma (Σ), is a concise way to express the sum of a sequence of terms. For example, Σ from i=1 to 5 of (a_i + 3b_i) means adding the values of a_i plus three times b_i for i = 1 through 5.

Using Graphs to Extract Sequence Values

Graphs of sequences plot term indices on the x-axis and term values on the y-axis. To find specific terms like a_i or b_i, locate the point at x = i and read the corresponding y-value. This skill is crucial for evaluating sums involving terms from graphical data.

In Exercises 61–68, use the graphs of and to find each indicated sum.∑i=15(ai+3bi)\(\sum\)_{i=1}^5(a_{i}+3b_{i})