Question 92400:
What are the next five terms in this sequence?:
3,10,5,16,8,4,2,1,4.... ???
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
What are the next five terms in this sequence?:
3,10,5,16,8,4,2,1,4.... ???
The recursive rule seems to be:
a1 = 3
If an is odd, use formula an+1 = 3an+1
If an is even, use the formula an+1 = an/2
So,
a1 = 3, which is odd, so a2 = 3a1+1 = 3(3)+1 = 9+1 = 10
a2 = 10, which is even, so a3 = a2/2 = 10/2 = 5
a3 = 5, which is odd, so a4 = 3a3+1 = 3(5)+1 = 15+1 = 16
a4 = 16, which is even, so a5 = a4/2 = 16/2 = 8
a5 = 8, which is even, so a6 = a5/2 = 8/2 = 4
a6 = 4, which is even, so a7 = a6/2 = 4/2 = 2
a7 = 2, which is even, so a8 = a7/2 = 2/2 = 1
a8 = 1, which is odd, so a9 = 3a8+1 = 3(1)+1 = 3+1 = 4
a9 = 4, which is even, so a10 = a9/2 = 4/2 = 2
a10 = 2, which is even, so a11 = a10/2 = 2/2 = 1
a11 = 1, which is odd, so a12 = 3a11+1 = 3(1)+1 = 3+1 = 4
a12 = 4, which is even, so a13 = a12/2 = 4/2 = 2
a13 = 2, which is even, so a14 = a13/2 = 2/2 = 1
a14 = 1, which is odd, so a15 = 3a14+1 = 3(1)+1 = 3+1 = 4
a15 = 4, which is even, so a16 = a15/2 = 4/2 = 2
After a5, which = 8, the terms go 4,2,1, over and over forever.
Edwin
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