common ratio
[common ratio|common ratio] is a numerical factor consistently multiplied to generate subsequent terms in a sequence.
Definition
common ratio is a numerical factor consistently multiplied to generate subsequent terms in a sequence.
Mechanism
common ratio The process begins with the first term, which is multiplied by the common ratio to generate the next term. This multiplication continues, producing each subsequent term through repeated application of the common ratio. The result of each multiplication determines the value of the following term in the sequence.
Causes
common ratio The sequence is geometric because there is a common ratio. This common ratio determines the relationship between consecutive terms. A consistent ratio between terms confirms the sequence's geometric nature.
Effects
common ratio determines the relationship between consecutive terms in a geometric sequence. Multiplying the previous term by this ratio produces the next term. The presence of a common ratio defines the sequence as geometric. This ratio directly influences the result of each subsequent term. A consistent common ratio ensures the sequence maintains its geometric progression.