Number Sequence Calculator
Identify arithmetic and geometric patterns in sequences and generate the subsequent terms automatically.
Type
Arithmetic
Common Difference
2
Next 5 terms
How to Use the Number Sequence Calculator
- Enter the starting sequence of numbers separated by commas.
- Specify how many next terms you want to generate (up to 20).
- The calculator identifies if the series is Arithmetic or Geometric and projects future terms.
Formulas & Principles
Arithmetic nth term: a_n = a₁ + (n - 1) × d
Arithmetic common difference: d = a_(k) - a_(k-1)
Geometric nth term: a_n = a₁ × r^(n - 1)
Geometric common ratio: r = a_(k) / a_(k-1)
Frequently Asked Questions
What is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant (d = a_(n) - a_(n-1)).
What is a geometric sequence?
An geometric sequence is a sequence where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio (r).
What formula finds the nth term of an arithmetic sequence?
The nth term is calculated using: a_n = a₁ + (n - 1) × d, where a₁ is the first term and d is the common difference.
Why this calculator matters
This calculator helps solve mathematical problems faster and with fewer manual arithmetic mistakes. It is useful for studying, research verification, technical engineering checks, and everyday problem-solving.
When to use it
Use it when you need a fast answer, a cross-check for manual calculations, or a clear step-by-step verification of your result.
Quick tips
Double-check your inputs, keep units consistent across all fields, and verify boundary conditions.
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