Math & Scientific
Geometric Sequence Calculator
Geometric Sequence: it uses the geometric-sequence formulas: nth term aₙ = a₁·r^(n−1) and sum Sₙ = a₁·(1 − rⁿ)/(1 − r). Worked through below with real figures, and the calculator repeats the working on your own inputs — free, on-device, instant.
Want to work through a calculation? Geometric Sequence Calculator does it from your first term, common ratio and term number and shows the result clearly, with everything calculated in your browser.
About this calculator
Geometric Sequence is easiest to get wrong in the setup, not the arithmetic. It uses the geometric-sequence formulas: nth term aₙ = a₁·r^(n−1) and sum Sₙ = a₁·(1 − rⁿ)/(1 − r). It matters when you need the exact relationship checked quickly rather than worked through by hand. The worked example on this page (For first term 2 and ratio 3, the 5th term = 2 × 3 4 = 2 × 81 = 162 .) shows the full substitution; the calculator above runs the same working on your own numbers, in your browser, with nothing uploaded.
How to use
- Enter the first term (a), the common ratio (r), and the number of terms (n).
- Press Calculate to run the geometric sequence calculator.
- Read the result: the nth term, the sum of the first n terms, and a preview.
- Press Reset to clear the geometric sequence calculator and start again.
Why use Geometric Sequence Calculator
Fast
Calculations run in your browser. No round trip to a server.
Private
Your inputs never leave your device. Nothing is uploaded.
Free
No signup, no paywall, no ads-in-results, no watermarks.
Accurate
Based on standard, well-established formulas.
Mobile-ready
Optimised for phones, tablets, and desktops alike.
Transparent
Honest disclaimers wherever browser limits or regional rules apply.
Common uses
Use it when revising for exams
Use it for double-checking a spreadsheet result
Geometric Sequence in tutoring and teaching sessions
Use it when preparing worksheets
Geometric Sequence in competitive-exam practice
Use it when comparing two different methods
Technical notes
Geometric Sequence Calculator uses the geometric-sequence formulas: nth term aₙ = a₁·r^(n−1) and sum Sₙ = a₁·(1 − rⁿ)/(1 − r).
Inputs are taken exactly as entered, so check for typos before trusting an answer.
All arithmetic runs in your browser using double-precision floating point, so extreme inputs may show tiny rounding differences.
FAQ
What is a geometric sequence?
A list of numbers where each term is multiplied by the same fixed value, called the common ratio (r).
How does the Geometric Sequence Calculator find the nth term?
Use aₙ = a₁ × r^(n−1); the calculator also returns the sum of the first n terms.
What do I enter in the Geometric Sequence Calculator?
The first term (a), the common ratio (r), and the number of terms (n).
Does the Geometric Sequence Calculator send my data to a server?
No — the Geometric Sequence Calculator runs entirely in your browser, so the numbers you enter never leave your device.
Worked example
For first term 2 and ratio 3, the 5th term = 2 × 34 = 2 × 81 = 162.