   Chapter 11.1, Problem 68E

Chapter
Section
Textbook Problem

# Find the first 40 terms of the sequence defined by a n + 1 = { 1 2 a n if   a n   is   an   even   number 3 a n + 1 if   a n   is   an   odd   number and a1 = 11. Do the same if a1 = 25. Make a conjecture about this type of sequence.

To determine

To find: The first 40 terms of the sequence.

Explanation

Given:

The sequence is an+1={12anif an is an even number3an+1if an is an odd number . (1)

Calculation:

Obtain the first 40 terms of the sequence when a1=11 .

 n an n an 1 11 21 22=1 2 3(11)+1=34 22 3(1)+1=4 3 342=17 23 42=2 4 3(17)+1=52 24 22=1 5 522=26 25 3(1)+1=4 6 262=13 26 42=2 7 3(13)+1=40 27 22=1 8 402=20 28 3(1)+1=4 9 202=10 29 42=2 10 102=5 30 22=1 11 3(5)+1=16 31 3(1)+1=4 12 162=8 32 42=2 13 82=4 33 22=1 14 42=2 34 3(1)+1=4 15 22=1 35 42=2 16 3(1)+1=4 36 22=1 17 42=2 37 3(1)+1=4 18 22=1 38 42=2 19 3(1)+1=4 39 22=1 20 42=2 40 3(1)+1=4

Therefore, the first 40 terms of the sequence when a1=11 are 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4.

Obtain the first 40 terms of the sequence when a1=25

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