Number Sequence Calculator
Adjust the inputs below. Results update as you type.
How it works
Arithmetic sequence: aₙ = a₁ + (n−1)d; common difference d is constant. Geometric: aₙ = a₁ × r^(n−1); common ratio r is constant. Fibonacci: aₙ = aₙ₋₁ + aₙ₋₂. Identify the type by checking if differences or ratios are constant. Sum of arithmetic series: n(a₁+aₙ)/2. Geometric series sum: a₁(1−rⁿ)/(1−r). Sequences appear in nature, finance, and algorithm analysis.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Arithmetic sequence: aₙ = a₁ + (n−1)d, with common difference d. Geometric sequence: aₙ = a₁ × r^(n−1), with common ratio r.
Worked example
The arithmetic sequence starting at 3 with d = 5 gives 3, 8, 13, 18… so the 10th term is 3 + 9×5 = 48.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
What is an arithmetic sequence?+
One where each term differs from the last by a constant amount (the common difference), like 2, 5, 8, 11.
What is a geometric sequence?+
One where each term is multiplied by a constant ratio, like 3, 6, 12, 24 (ratio 2).
How do I find the nth term?+
Use aₙ = a₁ + (n−1)d for arithmetic or aₙ = a₁·r^(n−1) for geometric, plugging in the position n.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.