SOLUTION: Please help me find a general term a sub n for the sequence 1/3, 2/4, 3/5, 4/6,...

Question 112934: Please help me find a general term a sub n for the sequence 1/3, 2/4, 3/5, 4/6,...
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Looking at the sequence of the numerators, we see: 1,2,3,4,...

And we can see that the numerators are increasing by 1 each time and start at 1. So if we start at n=0, then the general sequence for the numerators is:

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Looking at the sequence of the denominators, we see: 3,4,5,6,...

And we can see that the denominators are increasing by 1 each time, but are starting at 3. So if we start at n=0, then the general sequence for the denominators is:

So putting this all together we get

Notice if we let n=0, we get

If we let n=1, we get

If we let n=2, we get

And finally, if we let n=3, we get

So this verifies our answer.
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