Find the rates of change until it is constant...
dy/dx=7,16,25,34,43
d2y/dx2=8,9,9,9 so it appears 8 is the anomaly while the acceleration constant is 9 after the initial term. Let's set up a system ignoring the first data point and solve for the quadratic...
16a+4b+c=50
9a+3b+c=25
4a+2b+c=9 gettting differences
7a+b=25
5a+b=16 and again
2a=9, a=4.5, making 5a+b=16 become:
22.5+b=16
b=-6.5, making 4a+2b+c=9 become:
18-13+c=9, c=4
So the sequence can be expressed as:
a(n)=4.5n^2-6.5n+4, where n=term number