PROGRESSION

Progression

An arithmetic-geometric progression (AGP) is a progression in which each term can be represented as the product of the terms of an arithmetic progressions (AP) and ageometric progressions (GP).

Arithmetic Progression

For arithmetic sequences, the common difference is d, and the first term T₁ is often referred to simply as "a". Since you get the next term by adding the common difference, the value of T₂ is just a + d. The third term is T₃ = (a + d) + d = a + 2d. The fourth term is T₄ = (a + 2d) + d = a + 3d. Following this pattern, the n-th term a_n will have the form T_n = a + (n – 1)d.

the common difference d, is the difference between the last term and the first term, d=T_N-T_N-1

Geometric Progression

 For geometric sequences, the common ratio is r, and the first term a₁ is often referred to simply as"a". Since you get the next term by multiplying by the common ratio, the value of a₂ is just ar. The third term is a₃ = r(ar) = ar². The fourth term is a₄ = r(ar²) = ar³. Following this pattern, the n-th term a_n will have the form a_n = ar^{(n – 1)}.

the common ratio r, is the fraction of two the last term and the first term, r= T power of n/ T power (n-1)
                                                                                 SOURCE:http://www.basic-mathematics.com/