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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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Chapter
Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

DISCUSS A Recursively Defined Sequence Find the first 40 terms of the sequence defined by

a n + 1 = { a n 2 if a n is an even number 3 a n + 1 if a n is an odd number

and a 1 = 11 . Do the same if a 1 = 25 . Make a conjecture about this type of sequence. Try several other values of a 1 , to test your conjecture.

To determine

To find:

A conjecture about the given sequence and verify it for different initial values of the sequence.

Explanation

Approach:

Generate the first 40 terms using the initial data a1 and definition of the sequence and observe if sequence follows any pattern for large values of n.

Calculation:

There is given a table of sequence for the different initial values of a1.

Table (1)

We observe in the table above generated using excel for the sequence with different values of a1 that the sequence converges to a repeating sequence: 4,2,1,4,2,1,....

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Chapter 13 Solutions

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