The Common Ratio
Completion requirements
In geometric sequences, it is a
common ratio,
\(r \), that links
consecutive terms. Each successive term is found by multiplying the
previous term by the common ratio. A sequence is considered to be
geometric if the ratios between pairs of consecutive terms are constant,
which is similar to arithmetic sequences with their common differences.
Using variables, a geometric sequence can be written as:
\(t_1, t_1r, t_1r^2, ... , t_1r^{n - 1} \)
To determine the common ratio, \(r \), divide the second term by the first term of any pair of consecutive terms.
Using variables, a geometric sequence can be written as:
\(t_1, t_1r, t_1r^2, ... , t_1r^{n - 1} \)
To determine the common ratio, \(r \), divide the second term by the first term of any pair of consecutive terms.
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The Common Ratio
As a formula, the common ratio is written as:
\[r = \frac{{t_n }}{{t_{n - 1} }} \]
\(t_n\) is the second consecutive term
\(t_{n-1}\) is the first consecutive term