Question 238046
1) a list of numbers is even, find the next number by dividing by 2

2) if a number is odd , find the next number by multiplying by 3 and adding 1


if the first four numbers in the list are 14,7, 22,11, then the ninth number in the list is

a) 13 b) 9  c) 26  d) 40 e) none of these

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The first 9 go this way:

14, 7, 22, 11, 34, 17, 52, 26, 13

So the answer is choice a), 13.

The interesting thing about this sequence is that if it is
continued until a power of 2 appears, say {{{2^n}}}, then
the next term will be {{{2^(n-1)}}} and the next term {{{2^(n-2)}}}
and eventually it will get down to 1, then the next term will be 4,
then 2, then 1 again, and so then the terms 4,2,1,4,2,1,... 
will repeat forever.

This actually happens because the 14th term is 16 which is {{{2^4}}}

(1) 14  (2) 7  (3) 22  (4) 11  (5) 34  
(6) 17  (7) 52  (8) 26  (9) 13  
(10) 40  (11) 20  (12) 10  (13) 5  
(14) 16  (15) 8  
(16) 4  (17) 2  (18) 1  
(19) 4  (20) 2  (21) 1 
etc., etc.

By the way, I am very curious to know what mathematics course
you are taking that deals with such things as this.

Edwin</pre>