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Key Features
Instant Calculation
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An arithmetic sequence adds the same fixed amount at every step — simple in concept, but tedious to extend by hand once you need the 20th or 50th term. This calculator finds any term and the running sum of an arithmetic sequence directly from its first term and common difference, with a full step-by-step solution.
How it works
Enter the first term, the common difference between consecutive terms, and how many terms to generate. The calculator applies the nth term formula and the sum-of-n-terms formula directly, without manually adding term by term.
- Enter first term (a₁).
- Enter common difference (d).
- Enter number of terms (n).
- Click Calculate to see your results.
Examples
First term 3, difference 5, 10 terms
The sequence runs 3, 8, 13, 18, ..., 48 — the 10th term is 48, and the sum of all 10 terms is 255.
Who should use it
- Finding a specific term far into a sequence without manually adding the difference repeatedly.
- Checking arithmetic sequence homework problems for algebra or precalculus courses.
Industry applications
- Algebra and precalculus education
- Computer science (analyzing linear-growth patterns)
Advantages
- Calculates the nth term, the sum of n terms, and lists every term in the sequence.
- Uses the exact arithmetic sequence formulas, not iterative addition.
Limitations
- Limited to listing up to 100 terms at a time to keep the output readable.
Common mistakes to avoid
- Using (n) instead of (n − 1) in the nth term formula, which is an easy off-by-one error.
- Confusing an arithmetic sequence (constant difference) with a geometric sequence (constant ratio) — they use completely different formulas.
Best practices
- Double-check the common difference by subtracting two consecutive known terms before relying on a calculated nth term far into the sequence.
Tips
- If you're only given two terms of a sequence (not the first term and difference directly), find the common difference first, then work backward to the first term before using this calculator.