Formulas and properties of geometric sequence.
Definition Geometric sequence ( geometric progression) — a sequence of numbers b_{1}, b_{2}, b_{3}, ..., in which each member, starting with the second, equal to the product of the previous member and a constant number q ( common ratio), where b_{1} ≠ 0, q ≠ 0.
n -th term of the geometrical sequence is given by
b_{n} = b_{1} · q^{n - 1}
b_{n} = b_{n - 1} · q
A geometric series is the sum of the numbers in a geometric sequence.
Formulas of geometric series
S_{n} = |
b_{1} - b_{n + 1} | 1 - q |
S_{n} = b_{1} · |
1 - q^{n} |
1 - q |
Properties of geometric sequence
b_{n}^{2} = b_{n + 1} · b_{n - 1}
An infinite geometric series
If | q| < 1 and n → ∞
Add the comment |