Formulas of arithmetical and geometrical progressions

Arithmetic progression:

Progression's elements:

a1, a2, a3, ... , an

Progression's denominator:

d

Progression's element calculation formulas:

ai = ai+1d
i-th element of the progression calculation formula

Progression's n-th element calculation formula:

an = a1 + (n1) d

Sum of the first n-elements of progression formulas:

formula to calculate sum of the first n-elements of the arithmetic progression
formula to calculate sum of the first n-elements of the arithmetic progression

Geometric progression:

Progression's elements:

b1, b2, b3, ... , bn

Progression's denominator:

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

Progression's element calculation formulas:

bi+1 = bi q
bi2 = b i1 b i + 1

Progression's n-th element calculation formula:

bn = b1 q (n1)

Sum of the first n-elements of progression formula:

formula to calculate sum of the first n-elements of the geometric progression

Sum of the infinitely decreasing progression's formula:

formula to calculate sum of the infinitely decreasing geometric progression , | q | < 1

Other useful links:

Step by step solution of partial derivative sample
Logarithms formulas
Step by step solution of parametric derivative

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