note that these can be modeled with a quadratic function

how do we know that?

just look for when the difference between the terms become constant

stop since we get a constant difference of 2 between successive terms

so let (the function that gives the nth term, starting at n = 0)

with

.............(1)

.............(2)

.............(3)

thus you have a system with 3 equations and 3 unknowns, you can solve for