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Generate standard arithmetic sequences using the first term, common difference, and number of terms. Ideal for math studies, programming, and data analysis.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
An arithmetic sequence changes by the same amount between consecutive terms. Enter the first term, common difference, and number of terms to see the generated list, its final (nth) term, and the sum of the listed terms. The common difference can be positive, negative, or zero, so the sequence can increase, decrease, or repeat.
For first term a₁, common difference d, and term number n, the nth term is aₙ = a₁ + (n − 1)d. The sum of the first n terms is Sₙ = n(a₁ + aₙ)/2. The tool reports the sum and last generated term alongside the sequence.
With first term 4, common difference 3, and 5 terms, the sequence is 4, 7, 10, 13, 16. The fifth term is 4 + (5 − 1) × 3 = 16, and the sum is 5 × (4 + 16) ÷ 2 = 50. This quick check helps catch an off-by-one error: the first term is already term 1, so only n − 1 differences are added.
Term count is limited to 1–1,000 for the arithmetic mode. The displayed result can be copied, and the inputs can be shared using the page’s share controls.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Enter the first term. It may be an integer or decimal and may be negative.
Enter the common difference d. For example, d = −2 subtracts 2 at each step; d = 0 repeats the first value.
Enter an integer count from 1 through 1,000. A count of 1 returns just the first term, whose sum and nth term both equal that value.
Check the sequence, nth term, and sum together. Copy any displayed result you need for a worksheet or calculation note.
For a negative common difference, the sequence may cross zero. The sum can still be checked using the first and last terms in Sₙ = n(a₁ + aₙ)/2.
Use cases
See how the tool fits into real work and everyday tasks.
Generate several terms, then compare the final term and sum with the formulas used in class.
Explore a quantity that rises or falls by a fixed amount each period, such as a repeated weekly adjustment.
Try a negative difference and inspect the terms before relying on the total. Direction and starting term affect the result.
Q&A
Find concise answers to common questions and confusing cases.
It is the constant amount added to move from one term to the next. Subtract consecutive terms to check that the difference stays the same.
The shared progression page may offer a separate geometric mode, but this page is the arithmetic-sequence tool. For arithmetic results, the second input is the common difference.
When n = 1, there is only a₁. No differences are added, so the last term and total are both the first term.
Notes
Review scope, result limitations, and important precautions before use.
The arithmetic generator accepts a term count from 1 to 1,000. Its sum is the sum of the generated terms, not an infinite-series sum. Decimal inputs may produce decimal results. For work that requires exact rational arithmetic or a specified rounding convention, verify the displayed result with the precision required by that task.
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