Formulas of arithmetical and geometrical progressions

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Arithmetic progression:

Progression's elements:

a1, a2, a3, ... , an

Progression's denominator:

d

Progression's element calculation formulas:

ai+1 = ai + d
ai = ½ (ai1 + ai + 1)

Progression's n-th element calculation formulas:

an = a1 + (n1) d

Sum of the first n-elements of progression formulas:

Sn = ½ n (a1 + an)
Sn = ½ n (2 a1 + (n1) d )

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 = bi1 bi + 1

Progression's n-th element calculation formulas:

bn = b1 q (n1)

Sum of the first n-elements of progression formulas:

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

Sum of the infinitely decreasing progression's formula

formula to calculate sum of the infinitely decreasing progression