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)   (Show Source): You can put this solution on YOUR website!
, , , , , ...

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

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

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

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

So the recursive formuna for an is

a1 = 1, an+1 = ·an

Edwin
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