Arithmetic Sequence Calculator
How It Works
This arithmetic sequence calculator uses established formulas to provide accurate results.
The basic rule:
- aₙ = a₁ + (n-1)d
- Sₙ = n(a₁ + aₙ)/2
- Sₙ = n/2 · [2a₁ + (n-1)d]
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is an arithmetic sequence?
An arithmetic sequence is a list of numbers where each term increases (or decreases) by the same amount, called the common difference d. For example: 2, 5, 8, 11, 14 has d = 3.
How do I find the common difference?
Subtract any term from the next term: d = a₂ - a₁. In an arithmetic sequence, this difference is constant throughout.
How do I find the sum of an arithmetic series?
Use Sₙ = n(a₁ + aₙ)/2. This is the number of terms times the average of the first and last terms. It was famously used by Gauss to sum 1+2+3+...+100 = 100·101/2 = 5050.
What is the difference between a sequence and a series?
A sequence is the list of numbers (terms). A series is the sum of those numbers. The arithmetic sequence 2, 5, 8, 11 becomes the series 2 + 5 + 8 + 11 = 26.