Consider the sequence: n, F(n), F(F(n), F(F(F(n))) .... Construct the first 15 terms of the sequence for each of the following values of n: 6, 10, 15, 32 and 17

Question

Please help ASAP and if you can and places show me how you worked it out. I know it is probably easy but I can't figure it out

Answer 1

We have 5 different values of n to produce 15 terms of a sequence based on n and F for each value of n. So that's 5 series we have to produce.

F(n)=n/2 for n even, F(n)=(3(n)+1)/2 for n odd.

F(6)=3; F(3)=5; F(5)=8; F(8)=4; ...

The method is to apply F to each term to find the next.

Each series degenerates with the recurring pattern 1,2 (oscillating series).

The series is:

n=6: 6, 3, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1

n=10: 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2

n=15: 15, 23, 35, 53, 80, 40, 20, 10, 5, 8, 4, 2, 1, 2, 1

n=32: 32, 16, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2

n=17: 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2

Comments

Yes, it does help. So ignore this answer and I'll revise my answer later.

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