What is the equation for the following geometric sequence

Question

Geometric Sequence: (-10, -9, 0, 17)

What is the equation for the nth term for the geometric sequence above?

Answer 1

-10,-9,0,17, .. is not a GP. there is no common ratio

1st differences are

1, 9, 17

2nd differences are both

8

which suggests next term = 17+17+8 = 42

1st differences = 1, 9,17, 25

2nds = 8 8 and 8

no common ratio, but there is a common 2nd difference

an = 4n^2 -11n -3

a5 = 4(25) -11(5) -3 = 42

fit the points (1,-10), (2,-9),(3,0), (4,17) to a parabolic curve f(n) = y, a quadratic function