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Arithmetic Sequence Calculator | Compute Nth Term and Sum

Find the nth term and the sum of the first n terms of any arithmetic sequence, with the formula and working shown. Enter the first term and common difference and get any term in the sequence instantly.

Last updated: July 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

GivenFormulaExample (a₁=3, d=5, n=10)
nth termaₙ = a₁ + (n−1)da₁₀ = 3 + 9×5 = 48
Sum of n termsSₙ = n(a₁+aₙ)/2S₁₀ = 10(3+48)/2 = 255
Common differenced = a₂ − a₁8 − 3 = 5

info Arithmetic Sequence Calculator

Free math calculator — enter your numbers and get an instant, accurate result.

info Private by design

Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

Common difference dSequence behaviour
d > 0Increasing (3, 8, 13, …)
d = 0Constant — every term equals a₁
d < 0Decreasing (10, 7, 4, …)

lightbulb Worked example

Let's say you are using the Arithmetic Sequence Calculator. Finds the nth term and sum of any arithmetic sequence. Enter the first term, the common difference, and the position n you want, and the tool computes the nth term using the formula aₙ = a₁ + (n − Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ)/2 and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ)/2

The Arithmetic Sequence Calculator is built on a well-established calculation method. It uses the formula aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ)/2 to turn your inputs into a reliable result. Finds the nth term and sum of any arithmetic sequence. Enter the first term, the common difference, and the position n you want, and the tool computes the nth term using the formula aₙ = a₁ + (n − 1)d, plus the sum of The steps are shown on the page so you can follow the reasoning from input to output.

  1. Enter the first term a₁, the common difference d, and the term number n.
  2. The nth term comes from aₙ = a₁ + (n−1)d.
  3. The sum of the first n terms uses Gauss's pairing formula Sₙ = n(a₁+aₙ)/2.

Worked example: a₁ = 3, d = 5, n = 10 → a₁₀ = 3 + 9×5 = 48; S₁₀ = 10 × (3 + 48)/2 = 255. Sequence: 3, 8, 13, 18, 23, 28, 33, 38, 43, 48.

What is the Arithmetic Sequence Calculator?

The Arithmetic Sequence Calculator is a free, browser-based math calculator tool that helps you Finds the nth term and sum of any arithmetic sequence. Enter the first term, the common difference, and the position n you want, and the tool computes the nth t. Instead of working through the math by hand or in a spreadsheet, you enter your values and the calculator returns an accurate result instantly — while still showing the formula and the steps so you can verify the reasoning. It is designed for quick everyday use: no sign-up, no installation, and everything runs locally in your browser for complete privacy.

How to use the Arithmetic Sequence Calculator

  1. Enter the required values into the input fields.
  2. Press the calculate button — the result appears immediately, updated live as you change any value.
  3. Read the step-by-step breakdown below the result to see exactly how the calculation was performed.
  4. Use the interpretation guide to understand what the result means for your situation, and try different inputs to see how they change the outcome.

How to use the Arithmetic Sequence Calculator

Enter the first term, the common difference between consecutive terms, and the position n you want to find, then press calculate. The tool applies aₙ = a₁ + (n − 1)d for the nth term and Sₙ = n(a₁ + aₙ) ÷ 2 for the sum of the first n terms. For the sequence 2, 5, 8, 11, …, with a₁ = 2 and d = 3, the 10th term is 2 + 9 × 3 = 29 and the sum of the first 10 terms is 155.

Interpreting your result

The nth term formula describes the pattern — each term is the first term plus (n − 1) copies of the common difference. The sum formula adds the first and last term and multiplies by half the count, which is why it is sometimes called the 'average times count' method: the average of 2 and 29 is 15.5, times 10 terms is 155. Arithmetic sequences model anything that grows by a constant amount: monthly savings, seating rows, salary steps, and straight-line depreciation.

Common mistakes to avoid

The most common error is an off-by-one in the formula: the 10th term uses (10 − 1) = 9 differences, not 10. Second, using the sum formula with the wrong last term — Sₙ needs aₙ, the actual nth term, not a guess. Third, mixing up arithmetic (constant difference) with geometric (constant ratio) sequences — doubling 2, 4, 8, 16 is geometric, and the formula is different. Finally, forgetting that d can be negative, which makes the sequence decrease — the calculator handles that correctly.

Tips for best results

Identify a₁ and d first — everything else follows. To find the difference, subtract any term from the next one; verify it is constant across several gaps. When a problem gives you two terms without the first, solve for a₁ by working backward with the same formula. For sums of long sequences, the average-times-count shortcut is faster and less error-prone than adding term by term. If your terms multiply by a constant instead of adding one, switch to the geometric sequence calculator.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is an arithmetic sequence?
The Arithmetic Sequence Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Finds the nth term and sum of any arithmetic sequence. Enter the first term, the common difference, and the position n you want, and the tool computes the nth term using the formula aₙ = a₁ + (n − 1)d, plus the sum of the first n terms, with the working There is no limit on usage, and it works on any device.
What is the nth term formula?
The Arithmetic Sequence Calculator uses the standard aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ)/2. You enter your values, and the calculator applies the formula step by step, showing the working so you can verify the math and understand how the result is derived rather than trusting a black box.
How do you find the sum of an arithmetic sequence?
Enter the required values into the input fields and press the calculate button. The tool applies the formula aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ)/2 and returns the result with a short explanation of each step, so you can check the working yourself.
How do I find the common difference?
Subtract any term from the next one: d = aₙ₊₁ − aₙ. For 2, 5, 8, 11, the difference is 3. To confirm it is an arithmetic sequence, check that the gap is identical between several consecutive pairs. Once you have d and the first term, the formula aₙ = a₁ + (n − 1)d gives any term.
Can the common difference be negative or a fraction?
Yes — a negative common difference makes the sequence decrease (10, 7, 4, 1…), and a fractional difference produces fractional terms (0.5, 1.0, 1.5, 2.0…). The formulas work identically for both, and the calculator handles them with full precision. A zero difference makes every term equal, which is still a valid arithmetic sequence.
How do I find the common difference of a sequence?
Subtract any term from the one after it: for 7, 12, 17, 22 the common difference is 5. Check two or three gaps — if they differ, the sequence isn't arithmetic at all. A constant ratio instead of a constant gap (2, 6, 18, 54) means you're looking at a geometric sequence and need its tools.
How do I find the nth term without listing every term?
Use the formula aₙ = a₁ + (n − 1)d directly: for a₁ = 2 and d = 3, the 50th term is 2 + 49 × 3 = 149 — no listing needed. The calculator takes the first term, difference, and n, and returns the term plus the sum of the first n terms, so long sequences are solved in one step.
What does the Arithmetic Sequence Calculator do?
Finds the nth term and sum of any arithmetic sequence. Enter the first term, the common difference, and the position n you want, and the tool computes the nth term using the formula aₙ = a₁ + (n − 1)d, plus the sum of the first n terms, with the working. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Arithmetic Sequence Calculator use?
It uses aₙ = a₁ + (n − 1)d for the nth term and Sₙ = n(a₁ + aₙ)/2 for the sum of the first n terms, where d is the common difference. Enter the first term, the difference, and the position n, and the tool returns the nth term and the running sum, showing the step-by-step working.
Is the Arithmetic Sequence Calculator free and private?
Yes — the Arithmetic Sequence Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Arithmetic Sequence Calculator?
The Arithmetic Sequence Calculator applies the standard formula: aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ)/2. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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