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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

15-22 Arithmetic or Geometric? The first four terms of a sequence are given. Determine whether they can be the terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic or geometric, find the fifth term.

1 , 3 2 , 2 , 5 2 ,

To determine

The sequence 1,32,2,52, is an arithmetic sequence or a geometric sequence or neither and the fifth term 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 common difference which is the difference between two consecutive terms.

A geometric sequence is the sequence of the form,

a,ar,ar2,ar3,

Here, a is the first term and r is the common ratio which is the ratio of two consecutive terms.

Calculation:

Consider the sequence,

1,32,2,52,

Divide second term by first term of the above sequence,

a2a1=321=32

Divide third term by second term of the above sequence,

a3a2=232=43

The ratio of consecutive terms is not same, so, the sequence is not geometric

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