This is not an arithmetic or geometric sequence. It has no constant velocity, acceleration, or even thrust. You COULD make a higher order function fit each data point, however until you can actually find a constant rate of change at the higher orders it is not certain in any way that that function would predict the next term...
dy/dx=-5, -2, 7, 1, -4, -1 d2y/dx2=3, 9, -6, -5, 3 d3y/dx3=6, -15, 1, 8 d4y/dx4=-21, 16, 7 d5y/dx5=37, -9 d6y/dx6=-46 *note that the data never showed a constant rate of change
From above it can be seen that we COULD create a function to fit all of the points, but there would be no certainty in any way that that function would accurately predict the next number in the sequence.
ax^6+bx^5+cx^4+dx^3+ex^2+fx+g=y
And that would be a tedious amount of work to create that matrix to find a function that is essentially useless in predicting the next number in the sequence with any certainty...
