Formulas of arithmetical and geometrical progressions

Arithmetic progression:

Progression's elements:

a₁, a₂, a₃, ... , a_n

Progression's denominator:

d

Progression's element calculation formulas:

a_i = a_i+1 − d

Progression's n-th element calculation formula:

a_n = a₁ + (n − 1) d

Sum of the first n-elements of progression formulas:

Geometric progression:

Progression's elements:

b₁, b₂, b₃, ... , b_n

Progression's denominator:

q, if | q | < 1, then progression is called infinitely decreasing progression

Progression's element calculation formulas:

Progression's n-th element calculation formula:

b_n = b₁ q ^{(n − 1)}

Sum of the first n-elements of progression formula:

Sum of the infinitely decreasing progression's formula:

, | q | < 1