Find the nth term of this quadratic sequence 3,8,15,24,35...

n^2 + 2n.

Step-by-step explanation:

n       =       1     2     3     4     5

term t =     3    8     15   24   35

Diffs  =          5    7      9     11

                        2     2     2             - so the nth term contains n^2.

n^2   =       1     4      9    16    25

t - n^2 =    2    4      6     8     10

This is an arithmetic sequence with nth term = 2 + (n-1)2 = 2n

So the nth term of the quadratic sequence = n^2 + 2n.

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