Arithmetic Sequence Calculator
Calculate nth terms, sums, and find missing values in arithmetic sequences with detailed step-by-step solutions.
Calculation Type
Result
Enter the required values to calculate
Arithmetic Sequence Formulas
nth Term Formula
aₙ = a₁ + (n - 1) × d
Where: a₁ = first term, d = common difference, n = position
Sum Formula
Sₙ = n × (a₁ + aₙ) / 2
Or: Sₙ = n × (2a₁ + (n-1)d) / 2
Examples
Example 1: Even Numbers
Sequence: 2, 4, 6, 8, 10, ...
First term (a₁) = 2, Common difference (d) = 2
10th term: a₁₀ = 2 + (10-1) × 2 = 20
Example 2: Decreasing Sequence
Sequence: 100, 95, 90, 85, 80, ...
First term (a₁) = 100, Common difference (d) = -5
Sum of first 5 terms: S₅ = 5 × (100 + 80) / 2 = 450
Frequently Asked Questions
An arithmetic sequence is a sequence of numbers where each term after the first is obtained by adding a constant value (called the common difference) to the previous term. For example: 2, 5, 8, 11, 14... (common difference = 3).