Geometric progression

A sequence in which each term after the first is obtained by multiplying the previous term by a fixed number called the common ratio.

Common ratio: The fixed multiplier relating each term of a geometric progression to the preceding term. It is the single parameter that generates every term after the first.
Ratio: A comparison of two quantities expressed by division. The constant ratio between consecutive terms is the defining relation in a geometric progression.
Radioactive decay: The reduction of unstable atomic nuclei through spontaneous nuclear transformations. Over equal time intervals, the expected number of undecayed nuclei follows geometric decay.
Linear growth: Growth in which a quantity changes by a constant amount per unit of input or time. A geometric progression changes by a constant factor, so its increments generally are not constant.
Explicit formula: A rule that gives a sequence term directly from its index. For first term a and ratio r, it gives the nth term as a times r to the power n−1.
Exponentiation: The operation of raising a base to a power by repeated multiplication or its extensions. The nth term uses a power of the common ratio to encode repeated multiplication.
Binary search: A search algorithm that repeatedly halves a sorted range of possible locations. Its shrinking search interval forms a geometric progression, explaining logarithmic running time.
Fibonacci sequence: The sequence beginning 0, 1 in which each later term is the sum of the previous two. Its terms depend on addition of two predecessors, not one fixed multiplier.
Geometric series: The sum of the terms of a geometric progression, taken over a finite or infinite range. Adding progression terms produces a series with formulas governed by the same ratio.
Sequence: An ordered list of terms indexed by positive integers or another specified set. A geometric progression is a sequence distinguished by a constant quotient between consecutive terms.

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