Arithmetic Sequence Calculator
An arithmetic sequence changes by the same fixed difference between consecutive terms. Use this calculator to find a requested term and the sum of the first n terms.
How to use this calculator
- Enter the first term, fixed difference and positive term number. The output shows the chosen term and sum through that term.
- Check the labels and units before using a result outside this page.
- Change one input at a time if you want to compare scenarios.
Formula and method
aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ) ÷ 2
- aₙ = a₁ + (n − 1)d; Sₙ = n(a₁ + aₙ) ÷ 2
- The sequence must have a constant additive difference.
Worked examples
Worked example
First term 3, common difference 4, and term number 10.
a₁₀ = 3 + 9 × 4 = 39; S₁₀ = 10 × (3 + 39) ÷ 2 = 210.
a₁₀ = 3 + 9 × 4 = 39; S₁₀ = 10 × (3 + 39) ÷ 2 = 210.
Understanding the result
An arithmetic sequence changes by the same fixed difference between consecutive terms. Use this calculator to find a requested term and the sum of the first n terms.
The sequence must have a constant additive difference.
Important notes
The sequence must have a constant additive difference.
Displayed outputs are rounded for readability; preserve full precision when continuing a calculation.
Frequently asked questions
What does this arithmetic sequence calculator show?
An arithmetic sequence changes by the same fixed difference between consecutive terms. Use this calculator to find a requested term and the sum of the first n terms.
Which inputs should I check first?
Enter the first term, fixed difference and positive term number. The output shows the chosen term and sum through that term.
Can the result be used as a final professional specification?
The sequence must have a constant additive difference.
Related calculators
- Geometric Sequence Calculator — Calculate a term and finite sum in a mathematical geometric sequence with a constant ratio.
- Nth Root Calculator — Calculate a real integer-degree root, with domain checks for negative values and even roots.
- Series Resistance Calculator — Add two to four ideal resistances connected in series.
- Circle Calculator — Calculate circle area, circumference, and diameter from radius.
- Modulo Calculator — Find the normalized remainder from division for cycle, modular arithmetic, and number theory problems.
- Pythagorean Theorem Calculator — Find the hypotenuse of a right triangle from the two perpendicular sides.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- Percentage Change vs Percentage Difference — Understand the difference between percentage change and percentage difference, including when each formula is appropriate.
- How to Calculate Percent Error — Learn the percent error formula and how to compare an experimental value with a reference or accepted value.
- Percent Difference — Understand percent difference, when it is appropriate, and how it differs from percentage change and percent error.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.