Arithmetic Sequence Calculator

Solve aₙ = a₁ + (n−1)d ; Sₙ = n(a₁ + aₙ)/2 step by step — free arithmetic sequence calculator with worked examples, real-world defaults and instant answers.

aₙ = a₁ + (n−1)d ; Sₙ = n(a₁ + aₙ)/2

First term a₁Common difference dTerm number n

n-th term aₙ62

Sum of first n terms Sₙ670

Sequence start5, 8, 11, 14, 17, 20, 23, 26, …

1
Each term adds the common difference d, so the n-th term is:
aₙ = a₁ + (n−1)d = 5 + (20 − 1)(3) = 5 + 57 = 62
2
Gauss's pairing trick — first + last term, times n, halved:
Sₙ = n(a₁ + aₙ)/2 = 20(5 + 62)/2
3
Result:
Sₙ = 20 × 67 / 2 = 670

The sum formula is the famous schoolboy-Gauss insight: pairing the first and last terms gives n/2 identical pairs. It works for ANY arithmetic sequence — salaries with fixed raises, theatre rows, staircase bricks.

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Arithmetic sequence — nth term and partial sum from a₁ and common difference d.

About Arithmetic Sequence Calculator

The Arithmetic Sequence Calculator solves aₙ = a₁ + (n−1)d ; Sₙ = n(a₁ + aₙ)/2 for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. The sum formula is the famous schoolboy-Gauss insight: pairing the first and last terms gives n/2 identical pairs.

How to use Arithmetic Sequence Calculator

1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
2The tool substitutes them into aₙ = a₁ + (n−1)d ; Sₙ = n(a₁ + aₙ)/2 and recomputes live.
3Read the answer in the result box, then expand the step-by-step solution to see the full working.
4Copy the method into your notebook, or change inputs to explore how the result behaves.

Why use Arithmetic Sequence Calculator?

✓Solves aₙ = a₁ + (n−1)d ; Sₙ = n(a₁ + aₙ)/2 instantly as you type — no submit button, no waiting
✓Step-by-step solution shown for every calculation, not just the final answer
✓Realistic example values pre-loaded so you can see a worked example immediately
✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
✓Mobile-friendly and fast enough to use mid-homework or mid-lesson

Frequently asked questions

What formula does the Arithmetic Sequence Calculator use?+

It uses aₙ = a₁ + (n−1)d ; Sₙ = n(a₁ + aₙ)/2. The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.

What should I keep in mind when using this calculator?+

Is the Arithmetic Sequence Calculator free to use?+

Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.

Can I use this for homework, teaching or exam prep?+

That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.

Embed Arithmetic Sequence Calculator on your website

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