Choose a calculation for adjacent terms, nth terms, finite sums, or two indexed terms. The calculator shows convergent infinite sums with finite-sum results, requires integer indices, and reports both real ratios when indexed terms allow either sign.
What are common ratios?
The common ratio is the constant factor in a geometric sequence: multiply a term by the common ratio to get the next term.
A geometric sequence (also called a geometric progression) is a sequence of numbers where each term after the first is found by multiplying the previous term by the same constant. This constant is known as the common ratio.
Common Ratio Formula
The following equation is used to calculate the common ratio of a geometric sequence of numbers.
r = a(n+1) / a(n) (when a(n) ≠ 0). More generally, aₙ = a₁rⁿ⁻¹ for positive integer n. A zero denominator or even-power inverse may make a ratio nonunique; it must not be assigned a single arbitrary value.
- Where r is the common ratio
- a(n+1) is the term following a(n)
- a(n) is any term in the sequence
Common Ratio Example
How to calculate a common ratio?
First, determine the first, or an arbitrary number of a sequence. For this example, the first number of the sequence is found to be 12.
Next, determine the next number in the sequence following the number above. In this case, the number is found to be 36.
Finally, calculate the common ratio using the formula above:
r = a(n+1) / a(n)
r = 36 / 12
r = 3
FAQ
A common ratio is a term used to describe the ratio of consecutive terms in a sequence of numbers.
A geometric sequence (geometric progression) is a sequence where each term after the first equals the previous term multiplied by the same constant (the common ratio).
