MATH · NUMBER SEQUENCE
Number Sequence Calculator
Detect whether a number sequence is arithmetic, geometric, or Fibonacci-like, then extend it by up to 20 more terms.
About This Calculator
Identify the pattern in a number sequence and predict the next terms. Enter at least two numbers separated by commas. The calculator detects arithmetic (constant difference), geometric (constant ratio), and Fibonacci-like (each term = sum of the two before it) patterns, then extends the sequence by however many terms you request.
How It Works
The detection algorithm checks patterns in priority order: arithmetic first (constant d = aₙ − aₙ₋₁), then geometric (constant r = aₙ / aₙ₋₁), then Fibonacci-like (each term = sum of the previous two). All comparisons use a tolerance of 1e-9 to handle floating-point arithmetic. If none of the three patterns match, the sequence is marked as "unknown" and no extension is generated.
The Formula
Arithmetic: aₙ = a₁ + (n − 1)d Geometric: aₙ = a₁ · rⁿ⁻¹ Fibonacci: aₙ = aₙ₋₁ + aₙ₋₂
- a₁
- first term of the sequence
- d
- common difference (arithmetic)
- r
- common ratio (geometric)
- n
- term number (1-indexed)
Frequently Asked Questions
- What is an arithmetic sequence?
- An arithmetic sequence has a constant difference between consecutive terms. For example, 3, 7, 11, 15 has common difference d = 4. The nth term is a₁ + (n−1)d.
- What is a geometric sequence?
- A geometric sequence has a constant ratio between consecutive terms. For example, 2, 6, 18, 54 has common ratio r = 3. The nth term is a₁ · rⁿ⁻¹. Geometric sequences can grow or shrink exponentially and may have fractional ratios.
- What is a Fibonacci-like sequence?
- Any sequence where each term equals the sum of the two preceding terms follows the Fibonacci pattern. The original Fibonacci sequence starts 1, 1, 2, 3, 5, 8, 13 ... but any starting pair works — for example 2, 5, 7, 12, 19, 31 is also Fibonacci-like.
- Why does the calculator say my sequence is "unknown"?
- The calculator only detects arithmetic, geometric, and Fibonacci-like patterns. Many sequences (square numbers, primes, alternating, power-of-2) do not match these three forms, so they are labelled "unknown." Entering more terms sometimes helps if floating-point rounding caused a near-match to fail the equality check.