Can't find the pattern in a sequence of fractions

runryul

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Dec 15, 2019
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What is the 16th number in the pattern?

2/7 , 2/5 , 6/13 , 1/2 , 10/19 , 4/7 ...

I already know that the answer to this is 8/13 based on the answer key I am working with. However, I can't for the life of me figure out what the actual pattern is. Any help would be appreciated!
 
What if we try to rewrite each fraction so that the numerators are increasing?

2/7, 4/10, 6/13, 8/16, 10/19, 12/21, ...​
Does that have a pattern you can identify?

(Technically, if a pattern isn't explicitly stated, you really can't say anything about it, because there can be several equally reasonable "patterns" with the same first few terms. You're really just guessing. But my guess is no less valid than any other.)
 
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