What is the nth term rule of the quadratic sequence below? - 7, - 6, - 3, 2, 9, 18, 29, ...

Let the nth term be given by the expression an²+bn+c.

We can write A: - 7=a+b+c B: - 6=4a+2b+c C: - 3=9a+3b+c

D: B-A: 1=3a+b

E: C-B: 3=5a+b

E-Dm 2=2a, a=1, b=1-3=-2, c=-7-1+2=-6.

So the expression for the nth term is n²-2n-6.

Put n=4: 16-8-6=2 which fits the sequence.

Put n=5: 25-10-6=9 which also fits the sequence.

So the nth term is