About the geometric sequence calculator
In a geometric sequence each term is the previous one multiplied by a fixed common ratio r: 3, 6, 12, 24, … has r = 2. Enter any three of the first term, ratio, term number, nth term, sum or sum to infinity and the rest are found.
Finding r from two terms can have two answers, for a₁ = 2 and a₃ = 18, both r = 3 and r = −3 work, and both are shown.
Formulas
| nth term | aₙ = a₁·rⁿ⁻¹ |
| Sum of n terms | Sₙ = a₁(1 − rⁿ)/(1 − r) |
| Sum to infinity (|r| < 1) | S∞ = a₁/(1 − r) |
| Common ratio | r = (aₙ/a₁)^(1/(n−1)) |
Frequently asked questions
How do I find the nth term of a geometric sequence?
aₙ = a₁·rⁿ⁻¹. For 3, 6, 12, … the 8th term is 3·2⁷ = 384.
When does a geometric series have a sum to infinity?
Only when |r| < 1. The sum is then a₁/(1 − r).