Chapter 13.2, Problem 30E

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4th Edition

James Stewart + 2 others

ISBN: 9781305071742

Textbook Problem

**27-32 ■ Arithmetic Sequence? **Find the first five terms of the sequence, and determine whether it is arithmetic. If it is arithmetic, find the common difference, and express the nth term of the sequence in the standard form

To determine

The first five terms of the sequence *n*th term of the sequence in the standard form.

Explanation

**Approach:**

An arithmetic sequence is a sequence of the form,

Here,

The nth term of an arithmetic sequence in standard form is given by,

Here,

**Calculation:**

Calculate the first term of the sequence.

Substitute *n*th sequence to calculate the first term.

Calculate the second term of the sequence.

Substitute *n*th sequence to calculate the second term.

Calculate the third term of the sequence.

Substitute *n*th sequence to calculate the third term.

Calculate the fourth term of the sequence.

Substitute *n*th sequence to calculate the fourth term.

Calculate the fifth term of the sequence.

Substitute *n*th sequence to calculate the fifth term.

Therefore, the first five sequence is

Since in the arithmetic sequence, any two consecutive terms of the sequence differ by *d*

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