Good stuff. Your schools are better than ours.
9 22 41 66 97 134
13 19 25 31 37
6 6 6 6
They didn't ask but I'll tell you anyway when the second difference is constant that means we started from a second degree function, a quadratic function. We could figure it out, but they're saving that for the next part.
In the quadratic case, the coefficient of n² is half the second difference. So I'm writing a 3 in there.
I'll add an extra line for n to keep track; that's not part of the answer.
9 22 41 66 97 134
n 1 2 3 4 5 6
3 n² 3 12 27 48 75 108
subtr 6 10 14 18 22 26
Our difference follows the formula 4n+2 so our nth term of our original function is
Answer: 3n² + 4n + 2
Let's check a couple
f(n) = 3n² + 4n + 2
f(1) = 3+4+2=9, good
f(6) = 3(6²) + 4(6) + 2 = 108 + 24 + 2 = 134, good
