Question

Next no. in the sequence 7 2 0 7 8 4 3

Answer 1

7,2,0,7,8,4,3... in this order?

Answer 2

Any more information?

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...