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Arithmetic Sequence Calculator — nth Term, Sum & Common Difference

Arithmetic sequence calculator — nth term, sum of the first n terms, and the common difference from any two terms, all in your browser.

  • Runs locally
  • Category Calculator
  • Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.
Quick examples
Inputs
nth term · a₆ = a + (n-1)·d
17
Sum of first 6 terms · Sₙ
57
Terms
2, 5, 8, 11, 14, 17
Find the common difference from two terms
Two known terms and how many positions apart they are.
Common difference d3
Arithmetic vs geometric

An arithmetic sequence adds a fixed difference d each step (2, 5, 8, 11 — keep +3). A geometric sequence multiplies by a fixed ratio r each step (2, 4, 8, 16 — keep ×2). Adding makes arithmetic sequences grow in a straight line, while multiplying makes geometric ones curve up or decay fast, which is why simple counting and salary steps are arithmetic but compound interest is geometric.

What this tool does

A focused arithmetic sequence and arithmetic series calculator. Enter the first term a, the common difference d, and a count n, and read two answers at once: the nth term aₙ = a + (n-1)·d and the sum of the first n terms Sₙ = n(2a + (n-1)d)/2, which is the same as n(a + aₙ)/2. The tool lists the actual terms a, a+d, a+2d, a+3d, … so you can sanity-check the pattern by eye, and a one-click copy puts the whole sequence on your clipboard. A built-in reverse solver recovers the common difference from any two known terms and how many positions apart they sit, so if you only know the 1st term is 2 and the 4th is 11 it returns d = 3. Negative differences (a decreasing run like 20, 17, 14, 11) and fractional differences are handled, and a constant sequence with d = 0 still sums correctly to n·a. Everything runs locally in the browser with a shareable link that reopens the exact a, d and n you typed.

Tool details

Input
Numbers
The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output
Live result + Copy
The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy
Browser-side processing
The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share
Shareable URL state
Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget
Initial JS <= 9 KB
No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit
Calculator · Student
Category and role tags drive related tools, internal links, and quick fit checks.

How to use

  1. 1. Input

    Paste or drop your content into the tool panel.

  2. 2. Process

    Click the button. All processing is local in your browser.

  3. 3. Copy / Download

    Copy the result or download to disk in one click.

How Arithmetic Sequence Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

  • Getting a realistic range before a purchase, plan, workout, or schedule decision.
  • Comparing scenarios by changing one input at a time.
  • Turning rough assumptions into a number you can discuss.

Calculation checks

  • Double-check units, dates, rates, and rounding assumptions.
  • Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
  • Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

  1. 1 Geometric Sequence Calculator Geometric sequence calculator — nth term, sum of first n terms, and infinite series sum from first term a and common ratio r, all in your browser. Open
  2. 2 Number Sequence Generator Generate a list of numbers from start to end by step or count, with zero-padding, prefix, suffix and any separator, all in your browser Open
  3. 3 Fibonacci Generator First N terms, a range, or the nth value, with running sum and golden-ratio convergence, exact via BigInt, all in your browser Open

Real-world use cases

  • Verify the answer key for a quiz you wrote

    You set a quiz: a=5, d=4, find the 12th term and the sum of the first 12 terms. Type a, d and n in, read 49 and 324, and scan the listed terms to confirm none of the printed answers drifted. The copy button drops the full run into your answer sheet.

  • Sum a fixed monthly savings plan

    You save 100 the first month and add 25 more each month. Enter a=100, d=25, n=24 to see month 24's deposit (675) and the total banked over two years (18900), then share the link so a partner opens the exact same a, d and n.

Common pitfalls

  • Reading d off a list that is not arithmetic. If 2, 5, 8, 12 has gaps of 3, 3, 4, the steps are not equal and no single d describes it; the tool's formula assumes a constant difference.

  • Treating a fractional or negative d as invalid. a=1, d=0.5 and a=20, d=-3 are both fine; clearing the field instead of typing the decimal or minus sign leaves the result empty.

  • Expecting the sum to keep climbing when d is negative. With a=20, d=-3 the later terms go negative, so the partial sum can fall instead of grow as n increases.

Privacy

The nth term, the partial sum, the listed terms and the reverse-solved difference are all worked out in JavaScript inside this browser tab. Your a, d and n never travel to a server. Only the shareable link carries them, written into the URL query string, so paste that link only where you do not mind those three numbers being seen.

FAQ

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Made by Toolora · 100% client-side · Updated 2026-07-02