Ch. 8 - Sequences, Induction, and Probability

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

Blitzer 8th Edition

Ch. 8 - Sequences, Induction, and Probability

문제 14

9장, 문제 14

In Exercises 12–15, write the first six terms of each arithmetic sequence. a1 = 3/2, d = -1/2

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Step 1: Recall the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1) 	imes d

, where

a_1

is the first term,

d

is the common difference, and

n

is the term number.

Step 2: Identify the given values:

a_1 = \(\frac{3}{2}\)

(the first term) and

d = -\(\frac{1}{2}\)

(the common difference).

Step 3: Calculate the second term (

a_2

) using the formula:

a_2 = a_1 + d = \(\frac{3}{2}\) + (-\(\frac{1}{2}\))

. Simplify the expression to find

a_2

Step 4: Calculate the third term (

a_3

) using the formula:

a_3 = a_1 + 2d = \(\frac{3}{2}\) + 2(-\(\frac{1}{2}\))

. Simplify the expression to find

a_3

. Repeat this process for

a_4

a_5

, and

a_6

Step 5: Write the first six terms of the sequence in order:

a_1, a_2, a_3, a_4, a_5, a_6

, based on the calculations from the previous steps.

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주요 개념

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

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference (d). In this case, the first term (a1) is given, and the common difference allows us to generate subsequent terms by adding d to the previous term.

First Term and Common Difference

The first term of an arithmetic sequence is the initial value from which the sequence starts, denoted as a1. The common difference (d) is the fixed amount that is added to each term to obtain the next term. For the given sequence, a1 = 3/2 and d = -1/2, indicating that each term will decrease by 1/2 from the previous term.

Generating Terms of the Sequence

To find the terms of an arithmetic sequence, start with the first term and repeatedly add the common difference. For example, to find the first six terms, calculate each term by applying the formula: a_n = a1 + (n-1)d, where n is the term number. This process allows for systematic generation of the sequence's terms.