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