Arithmetic Sequence Calculator
List every term, find the Nth term and sum an arithmetic sequence from its first term and difference or any two known terms — fractions and decimals work too.
Fractions such as 5/2 are fine.
2, 5, 8, 11, 14
14
40
What this arithmetic sequence calculator does
Enter the first term, the common difference, and how many terms you want, and this tool instantly lists the whole sequence, highlights the Nth (last) term, and adds everything up into a total. An arithmetic sequence is any list of numbers where each term is found by adding the same fixed amount — the common difference — to the one before it, such as 2, 5, 8, 11, 14. The difference can be positive, negative, or zero, and both the first term and the difference may be decimals or fractions such as 5/2, so the calculator works for whole numbers and fractions alike. If you know two terms instead — say the third and the seventh — set "Start from" to "Two known terms" and it works out the difference and the first term from them. If each term is instead the one before multiplied by a fixed ratio, use the Geometric Sequence Calculator.
The formulas behind the results
The Nth term is computed directly with a₁ + (N − 1) × d, so you get the value of the last term without walking through every step. The sum uses the closed-form series formula N / 2 × (2 × a₁ + (N − 1) × d), which is far faster and more precise than adding the terms one by one. Everything recalculates live as you type, and each result has its own copy button. A "Working" block under the answers shows each formula with your own numbers in it, a chart draws the terms, and "Decimal places" rounds every answer to the places you choose. Each answer also has its formula printed beside it. The “Worked examples” buttons load three textbook questions — Gauss's sum of the first hundred whole numbers, an nth term from a₁ and d, and d from two known terms — so the Working block solves each one line by line. To keep the listing readable and responsive, the list is limited to 1000 terms, but a larger N is still answered: the Nth term and the sum count every term, and a line says how many are listed. Untick "List the terms" to see the two answers on their own. “Save this calculation” keeps it in this browser under “Saved calculations”, where it can be opened again or deleted.
Frequently asked questions
How is the Nth term different from the sum?
The Nth term is one number, where the list stops: a₁ + (N − 1) × d. The sum adds all N terms, and the Working block computes it as N × (a₁ + a_N) ÷ 2 — the first and last terms averaged, times how many there are.
Can the common difference be negative or a decimal?
Yes. A negative difference produces a decreasing sequence, a difference of zero repeats the first term, and decimals are fully supported for both the first term and the difference. Results are rounded to the number of decimal places you entered, so a₁ 0.1 with d 0.2 lists 0.3 rather than 0.30000000000000004.
Can I find the sequence from two terms I know?
Yes. Set "Start from" to "Two known terms" and fill in "Position p", "Term at p", "Position q" and "Term at q": the difference is (a_q − a_p) ÷ (q − p), the first term follows from it, and the "Working" block prints both lines with your numbers. The positions have to be different whole numbers from 1 up, and "Number of terms (N)" still says how many terms to list.
Can I get the sum of more terms than the page lists?
Yes. The Nth term and the sum count every term however large N is, as long as the count is still exact; only the list stops, and a line says how many terms it shows. Untick "List the terms" to see the two answers on their own, each with its formula printed beside it.
Are there worked examples to learn from?
Yes. “Worked examples”, under the inputs, has three buttons: Gauss's sum of the whole numbers from one to a hundred, an nth term from a₁ and d, and d from two known terms. Each one fills the boxes, and the Working block below then solves it line by line with those numbers.