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 , then
the next term will be and the next term
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
(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