Formulas and properties of geometric progression

Geometric progression is a number sequence b1, b2, b3, ..., in which each subsequent number, starting from the second, is obtained from the previous one by multiplying it by a certain number q (the common ratio of the progression), where b1 ≠ 0, q ≠ 0.

n-th term of a geometric progression

bn = b1 · qn-1

an = an-1 · d

Common ratio of a geometric progression

q = bn bn-1

Sum formulas of a geometric progression

Sn = b1 - bn+1 1 - q
Sn = b1 · 1 - qn 1 - q

Property of a geometric progression

bn2 = bn+1 · bn-1

Sum of an infinite geometric progression

If |q| < 1 then as n → ∞.

S = b1 1 - q
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