Calculators
Arithmetic Sequence Calculator
Find the nth term and sum of an arithmetic sequence from its first term and common difference, privately in your browser.
Find terms and sums for a constant difference.
An arithmetic sequence adds the same common difference d at each step. The nth term is aₙ = a₁ + (n − 1)d and the sum of the first n terms is Sₙ = n(a₁ + aₙ) / 2. For a first term of 3, difference of 2, and 10 terms, the last term is 21 and the sum is 120. Negative differences describe decreasing sequences; a zero difference gives a constant sequence. Enter finite signed numbers for the first term and difference, and a whole number from 1 to 1,000,000 for n. The preview shows at most the first ten terms. Calculations use browser floating-point arithmetic and display up to 12 significant digits, so very large values or tiny differences may lose precision. This tool does not infer a pattern from a list or calculate geometric sequences. All processing stays in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How do I find the nth term?
Use aₙ = a₁ + (n − 1)d. Starting at 3 with a difference of 2, the tenth term is 3 + 9 × 2 = 21.
How do I calculate the sum?
Multiply the number of terms by the average of the first and last terms: Sₙ = n(a₁ + aₙ) / 2. The first ten terms of 3, 5, 7, … sum to 120.
Can the difference be negative or zero?
Yes. A negative difference produces a decreasing sequence, and zero produces a constant sequence. The first term may also be negative or zero.
Which inputs and precision are supported?
Enter finite signed decimals or scientific notation for the first term and difference. The term count must be a whole number from 1 to 1,000,000. Results show up to 12 significant digits using floating-point arithmetic. Your values stay in your browser.