Question

Hi, I can't figure this one out:

Here are the first 5 terms of a sequence {5/3, 7/8, 9/15, 11/24, 13/35....}
a) Find the general term.

So far I got the top part of the fraction as (2n+3), but I can't figure out how to get the bottom one. I see a pattern where I have for n=1 (3*1), for n=2 (4*2), for n=3 (5*3), for n=4 (6*4), for n=5 (7*5), but I don't know how to translate it into an nth term.

Thank you

Answer 1

for the denominator ... n * (n + 2) = n^2 + 2n