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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

5-10 Terms of an Arithmetic Sequence The n t h term of an arithmetic sequence is given.(a) Find the first five terms of the sequence. (b) What is the common difference d ? (c) Graph the terms you found in part (a).

a n = 6 4 ( n 1 )

To determine

(a)

The first five terms of the sequence.

Explanation

Approach:

An arithmetic sequence is a sequence of the form,

a,a+d,a+2d,a+3d,a+4d,

Here, a is the first term and d is the difference between two consecutive terms.

Given:

The nth term of an arithmetic sequence is given as,

an=64(n1)

Calculation:

Calculate the first term of the sequence.

Substitute 1 for n in the nth sequence to calculate the first term.

a1=64(11)=6

Calculate the second term of the sequence.

Substitute 2 for n in the nth sequence to calculate the second term.

a2=64(21)=64=10

Calculate the third term of the sequence.

Substitute 3 for n in the nth sequence to calculate the third term.

a3=64(31)=68=14

Calculate the fourth term of the sequence

To determine

(b)

The common difference of the sequence.

To determine

(c)

To sketch:

The graph of the arithmetic sequence.

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