What is the difference of arithmetic progression to geometric progression?

Answer 1

In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant.

That is,

Arithmetic progression

U(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ...

Equivalently,

U(n) = U(n-1) + d = U(1) + (n-1)*d

Geometric progression

U(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ...

Equivalently,

U(n) = U(n-1)*r = U(1)*r^(n-1).