Answer:
2n^2+n-3, 663
Step-by-step explanation:
This is the same as having (1, 0), (2, 7), (3, 18), (4, 33), (5, 52)
We know that this is a parabola because the difference of the differences is a constant:
7, 11, 15, 19
4, 4, 4
this means the nth term is an^2+bn+c
we know a = 2 because the 2a is the difference's difference of 4, 4/2 = 2
now we plug in points to find the others:
2*1^2 + b*1 + c = 0 = 2 + b + c
so b + c = -2
2*2^2 + b*2 + c = 7 = 8 + 2b + c
so 2b + c = -1
2b + c - (b + c) = -1 - - 2 = b = 1
so b = 1
b + c = -2 = 1 + c
c = -3
we put these together to get our answer
2n^2 + n - 3
for 18 this is 2 * 18^2 + 18 - 3 = 663
