SOLUTION: What is the next fraction in this sequence? Simplify your answer. 1/72, 1/36, 1/18, 1/9

Algebra ->  Sequences-and-series -> SOLUTION: What is the next fraction in this sequence? Simplify your answer. 1/72, 1/36, 1/18, 1/9       Log On


   

Question 1086899: What is the next fraction in this sequence? Simplify your answer.
1/72, 1/36, 1/18, 1/9

Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
If the common denominator is changed to 72, the numerators are 1,2,4, and 8. Therefore, the next numerator is 16 and the common denominator is 72
16/72=2/9

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F72, 1%2F36, 1%2F18, 1%2F9+
this is a geometric sequence
if we first term multiply by 2, we will get second term
%281%2F72%292=2%2F72=1%2F36...do same with second term to get third term
%281%2F36%292=2%2F36=1%2F18,
%281%2F18%292=2%2F18=1%2F9
next fraction is:
%281%2F9+%292=2%2F9
%282%2F9%292=4%2F9
so, sequence is
1%2F72, 1%2F36, 1%2F18, 1%2F9,+2%2F9, 4%2F9, 8%2F9, 16%2F9, 32%2F9, ...
general formula:
a%5Bn%5D+=+2%5E%28n+-+4%29%2F9+