Number Sequence Calculator
Generate arithmetic, geometric, Fibonacci, and custom sequences. Find the nth term and sum.
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Generate arithmetic, geometric, Fibonacci, or custom-formula number sequences, and instantly see the nth term, the running sum, and a full term-by-term table.
How Number Sequence Calculator Works
An arithmetic sequence adds the same fixed amount (the common difference, d) to get each next term, so the nth term equals a₁ + (n−1)d. A geometric sequence instead multiplies by a fixed common ratio r each time, so its nth term equals a₁ × r^(n−1) — arithmetic sequences grow at a constant rate, while geometric sequences grow (or shrink) exponentially.
The Fibonacci mode starts with two 1s and generates every following term as the sum of the previous two, a pattern that appears throughout nature, from spiral shell growth to branching plants. Custom mode lets you type any formula using the variable n (like n²+1), which is evaluated fresh for every position from 1 up to however many terms you request.
The sum (Sₙ) is calculated by directly adding every generated term together — a straightforward approach that works correctly for any sequence type or custom formula, rather than relying on a closed-form shortcut that would only apply to arithmetic or geometric sequences specifically.
See It In Action
Who Uses Number Sequence Calculator and Why
- Generating the terms of an arithmetic or geometric sequence for an algebra assignment.
- Exploring the Fibonacci pattern for a nature or biology project on spiral growth.
- Testing a custom formula like n²+1 to see how a non-standard sequence behaves term by term.
- Getting the running sum of a sequence's terms without deriving a separate closed-form sum formula by hand.
Mistakes to Avoid
- Expecting the Fibonacci sequence to start 0, 1 — this calculator uses the 1, 1, 2, 3, 5 convention, which is equally valid but different from some textbooks.
- Typing a custom formula with the wrong operator syntax (like ^ instead of **) so the expression doesn't evaluate as intended for each value of n.
- Assuming a negative common ratio in a geometric sequence just shrinks the values — it actually makes the terms alternate between positive and negative while changing in magnitude.
Tips for Best Results
- If comparing results against a textbook's Fibonacci sequence, check which starting convention (0,1 or 1,1) it uses before assuming a mismatch is an error.
- In custom formula mode, use n exactly as the variable name — the calculator substitutes each position from 1 up to your term count directly into your typed expression.
Fixing Common Problems
My Fibonacci sequence doesn't match my textbook. — Check the starting convention — this calculator begins with 1, 1 rather than 0, 1. Both are standard, just different starting points for the same recurring pattern.
Terms Explained
Common difference: The fixed amount added to each term to get the next one in an arithmetic sequence.
Common ratio: The fixed multiplier applied to each term to get the next one in a geometric sequence.