SOLUTION: write a recursive rule for the sequence 1, 1/2, 1/2, 3/4, 3/2,...

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Question 862879: write a recursive rule for the sequence 1, 1/2, 1/2, 3/4, 3/2,...
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
1, 1%2F2, 1%2F2, 3%2F4, 3%2F2, ...

1st term = 1, then
multiply the 1st term, 1, by 1%2F2 to get the 2nd term, 1%2F2, 
multiply the 2nd term, 1%2F2, by 1 to get the 3rd term, 1%2F2, 
multiply the 3rd term, 1%2F2, by 3%2F2 to get the 4th term, 3%2F4, 
multiply the 4th term, 3%2F4, by 2 to get the 5th term, 3%2F2 

Notice that if we think of 1 as 2%2F2 and 2 as 4%2F2, we have:

1st term = 1, then we
multiply the 1st term, 1, by 1%2F2 to get the 2nd term, 1%2F2, 
multiply the 2nd term, 1%2F2, by 1%2F2 to get the 3rd term, 1%2F2, 
multiply the 3rd term, 1%2F2, by 3%2F2 to get the 4th term, 3%2F4, 
multiply the 4th term, 3%2F4, by 4%2F2 to get the 5th term, 3%2F2 

So we multiply the nth term by n%2F2 to get the (n+1)st term. 

So the recursive formuna for an is

a1 = 1, an+1 = n%2F2·an

Edwin