數學題一問 (2)

Question

A sequence of numbers has 2 as its first term, and every term after the first is defined as follows:

if a term, t, is even, the next term in the sequence is 1/2t. If a term, s, is odd the next term is 3s+1. Thus, the first four terms in the sequence are:12,6,3,10. Find the 1000th term of the sequence.

the ans is probably 4 but how to show the steps? pls explain

Answer 1

最愛解答

The first few terns are 12,6,3,10,5,16,8,4,2,1,4,2,1,4,2,1....

From the 8th term it is 4, and repeated every 3 terms. Then for 1000th, (1000-7)/3=993/3=330, no reminder, so the 1000th term is 1. If 2 is the first term, then 2,1,4,2... for 1000th term, (1000-2)/3=998/3=332....2, the 1000th term is 2.