Arithmetic Sequence Calculator

About the Arithmetic Sequence Calculator

An arithmetic sequence is a sequence in which the difference between any two adjacent terms (the common difference) is the same. The arithmetic sequence calculator is an intelligent math tool that, given any three known parameters, automatically computes the other two unknown parameters of the sequence. It supports all possible parameter combinations and shows detailed steps to help you understand the calculation.

Supported Combinations

• Given a, d, n → computes an, sn
• Given a, an, n → computes d, sn
• Given a, d, sn → computes n, an
• Given a, an, sn → computes n, d
• Given d, n, sn → computes a, an

How to Use

1. Enter any three parameters (such as the term count n, first term a, and common difference d).
2. Click the "Calculate" button (or press Enter).
3. View the results: the remaining two parameters are filled in automatically, along with detailed calculation steps.
4. Use an example: click the "Example" button to get a random sample (two parameters are left blank automatically).
5. Click the "Clear" button to reset all inputs.

Basic Formulas

• Common difference (d): d = an - a(n-1)
• nth term formula: an = a1 + (n-1) × d
• Sum of the first n terms: Sn = n/2 × (a1 + an) or Sn = n/2 × [2a1 + (n-1)d]