Geometric Sequence
Find nth term and sum of a geometric progression
Working out find nth term and sum of a geometric progression is easier with Geometric Sequence — a free tool that does the math for you. You provide First Term (a₁), Common Ratio (r) and Number of Terms; the tool does the rest in real time. Every answer includes a transparent breakdown you can repeat by hand. It is handy for quick estimates at work, at home, or on the go. No sign-up, no server storage — the math happens right on your device, and most tools work offline after the first visit. It is part of the Math collection on CalcProMaster, alongside geometric sequence calculator nth term sum, free online geometric sequence calculator and more. Bookmark it and the answer is always one click away.
What does the page calculator do?
Geometric Sequence works out the nth term from the First Term, Common Ratio, and Number of Terms, following standard Math conventions — the page defaults produce a nth term of aₙ=162.00 | Sₙ=242.00.
- Inputs: First Term, Common Ratio, and Number of Terms.
- Output: the nth term, plus the intermediate steps behind it.
- Method: the standard Math formula, evaluated entirely in your browser.
Quick answer
With the default inputs (first term of 2, common ratio of 3, number of terms of 5), geometric sequence returns a nth term of aₙ=162.00 | Sₙ=242.00. Assumptions and limits are summarized below.
How does it work?
Geometric Sequence computes the nth term directly from your inputs — the First Term, Common Ratio, and Number of Terms feed the formula. Nothing is uploaded: the math runs locally in your browser and the result appears as you type.
How it works
Geometric Sequence answers one question well — given the values you provide, what is the nth term? Enter the First Term, Common Ratio, and Number of Terms, and the result panel returns the value with the full working underneath.
Using the Geometric Sequence
- First Term — one of the values the calculation builds from; the result reflects exactly what you type here.
- Common Ratio — used in the first stage of the calculation, so entering it accurately matters more than any later refinement.
- Number of Terms — the value that feeds directly into the formula — match it to the scenario you are modeling before moving on.
- Note the nth term. It updates as you type, and the worked steps below it make the arithmetic auditable.
- Iterate. Vary the inputs one at a time; the movement in the output shows which lever matters most for your geometric sequence question.
The formula behind the result
The relationship between the inputs is fixed by the formula, and Geometric Sequence makes each substitution explicit so nothing about the nth term is hidden.
Worked example: with first term of 2, common ratio of 3, number of terms of 5, this geometric sequence calculation returns aₙ=162.00 | Sₙ=242.00. The same run reports r=3 | n=5.
The steps it follows:
- aₙ = a₁·r^(n-1) = 2×3^4 = 162.00
- Sₙ = a₁(rⁿ-1)/(r-1) = 242.00
Substitute your own values and the same steps produce your answer — that is the point of a calculator that shows its working.
Understanding the result
To interpret the result from geometric sequence, read it together with the intermediate figures — the pairing is what makes the number auditable.
Where it helps
Geometric Sequence fits planning and checking: short-term planning, comparing scenarios side by side, and double-checking the nth term, or any moment when the nth term needs to be right the first time.
Common mistakes
The most common error with Geometric Sequence is a unit mismatch — one value entered in different units than its label assumes quietly skews the nth term. Check each label before typing.
Tip: Run Geometric Sequence twice with deliberately low and high inputs; the spread tells you how sensitive the result is, which a single run never shows.
Assumptions and limitations
Results from Geometric Sequence are estimates computed from the values entered; real-world outcomes can differ when fees, taxes, or conditions not modeled here apply.
Why use this calculator
Because the page doubles as documentation: Geometric Sequence puts the formula, a worked example, and the assumptions right beside the calculator.
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Frequently Asked Questions
What does the tool calculate?
Geometric Sequence is built for geometric sequence questions that need a defensible number: the working is always visible, the inputs accept your own values, and the nth term updates as you type. Because the working is visible: Geometric Sequence shows each operation behind the output in the steps panel, so you can verify the result instead of trusting a black box.
How is the nth term calculated?
The first steps are aₙ = a₁·r^(n-1) = 2×3^4 = 162.00, then sₙ = a₁(rⁿ-1)/(r-1) = 242.00. Geometric Sequence lists every intermediate step in the result panel, so the derivation of the figure can be checked line by line.
What do I need to use the Geometric Sequence?
The First Term, Common Ratio, and Number of Terms it asks for, or the page defaults if you just want to see the calculation work. Each input maps directly to the formula, and changing any one of them recalculates the nth term instantly.
What does the result from the tool mean?
The main number the geometric sequence returns is the nth term for your exact inputs, and the supporting figures and step list give it context. Geometric Sequence assumes the units shown in each label — entering values in different units will skew the nth term proportionally.
When is the page most useful?
Typical uses for Geometric Sequence include short-term planning, comparing scenarios side by side, and double-checking the nth term — anywhere the figure needs to be defensible rather than guessed. If the nth term looks wrong, read the steps panel before re-entering anything; it usually shows exactly where the number departed from expectation.