Question

find the sequence of 10,12,15,19 ,?

Answer 1

try constructing a difference tier

Answer 2

each row is the difference of the terms above it:

a0 a1 a2 a3 a4 a5
b0 b1 b2 b3 b4
c0 c1 c2 c3

once you get down to a row of a constant term ... your at the end

the resulting equation for the sequence, for n=0,1,2,3,... is then constructed from the first elements:\[a_o+b_o~n+c_o\frac{n(n-1)}{2!}+d_o\frac{n(n-1)(n-2)}{3!}+...\]