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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

33-44 Terms of an Arithmetic sequence Determine the common difference, the fifth terms, the n th terms and the 100 th term of the arithmetic sequence.

4 , 10 , 16 , 22 ,

To determine

The common difference, the fifth terms, the nth terms and the 100th term.

Explanation

Given:

The arithmetic sequence 4,10,16,22,.

Approach:

The common difference of an arithmetic sequence is the difference between two consecutive terms.

An arithmetic sequence is a sequence of the form,

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

Where, a is the first term of the sequence and d is the common difference of the sequence.

The nth term of the arithmetic sequence is given by,

an=a+(n1)d...(1)

Calculation:

Consider the sequence,

4,10,16,22,

The first term of the sequence, a is 4.

The common difference of the sequence is,

d=104=6

The fifth term of the sequence is,

a5=22+d

Substitute 6 for d in above equation,

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