Question

Can you please answer me

Answer 1

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