Geometric Sequence Calculator
Compute the nth term, finite sum and (if |r|<1) infinite sum of a geometric sequence.
Input Data
First Term
Common Ratio
Term Count
Results
The Nth term.
512
Sum of first N terms.
1,023
Infinite Sum
0
At a glance:a_N = a1·r^(N−1); finite sum = a1(1−r^N)/(1−r); infinite sum = a1/(1−r) when |r|<1. Complements geometric-seq and sequence.
Formula
a_N = a1·r^(N−1).
infinite S = a1/(1−r) for |r|<1.
$$a_n = a_1 r^{n-1}$$$$S_n = a_1 \frac{1-r^n}{1-r}$$$$S_\infty = \frac{a_1}{1-r} \quad (|r|<1)$$How to Use
- Enter first term, ratio and N.
- The tool returns the Nth term, finite and infinite sums.
Case Studies
a1=1, r=0.5
finite N=4 = 1.875; infinite = 2.
FAQ
When does the infinite sum exist?
Only when |r|<1; otherwise it diverges.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.