The first few terms are
-6 -2 12 36 70
And using the sum of differences, we have :
-6 -2 12 36 70
4 14 24 34
10 10 10
This will be a 2nd power polynomial in the form an^2 + bn + c
And we have this system
a + b + c = -6
4a + 2b + c = -2
9a + 3b + c = 12
Subtract the frist equation from the second and the second equation from the third and we have
3a + b = 4
5a + b = 14 subtract the first equation from the second
2a = 10
a = 5
And using 3a + b = 4 ⇒ 3(5) + b = 4 ⇒ b = -11
And using a + b + c = -6 ⇒ 5 - 11 + c = -6 ⇒ -6 + c = -6 ⇒ c = 0
So....the polynomial is
5n2 - 11n
