the quadratic model for the sequence is a03 a2 a636 the quad

Solution

assuming that a₂=0

f(A) = lA^2 + mA + n

When A0=3 So n = 3.

So we know now

f(A) = lA^2 + mA + 3

A2=0 so 4l + 2m + 3 = 0 eqn(1)
A6=36 so 36l + 6m + 3 = 36 eqn(2)

multiply eqn(1) by 3 and subtract from eqn(2):

so 24l - 6 = 36 ie l = 7/4 substitute this back in eqn(1):

7 + 2m + 3 = 0 hence m = -5

So quadratic model is

f(A) = (7/4)A^2 - 5A + 3