if p is the nth term

8+20+52+.....+p
evaluate the sum to n-of the series

plz show step

3 answers

Looking at only 3 terms,
they are not in AP
they are not in GP

looking for some pattern:
8 = 4*2
20 = 4*5
52 = 4*13

I see nothing special about 2, 5, 13
2 = 1+1
5 = 4+1
13 = 12+1

still nothing
There are lots of sequences that fit those three numbers. Possibly the simplest is a quadratic,

10x^2-18x+16

So,

p
∑ 10x^2-18x+16 = 2/3 p(5p^2-6p+13)
k=1
Of course, why didn't I think of that

2 data values --- linear
3 data values --- quadratic
4 data values --- cubic
etc