Number Sequence Calculator
Enter the first four terms of a sequence and this calculator detects whether it is arithmetic (constant difference) or geometric (constant ratio), then extends it by three terms, states the rule and evaluates the nth term.
TheCalculators — Number Sequence Calculator
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Next 3 terms
14, 17, 20
Arithmetic sequence · common difference d = 3
- Pattern
- Arithmetic (constant difference)
- Common difference (d)
- 3
- Rule
- aₙ = a₁ + (n − 1)·d = 2 + (n − 1)·3
- Term #10 (aₙ)
- 29
- Next 3 terms
- 14, 17, 20
- Differences checked
- 3, 3, 3
Pattern detection
- 1Differences between termsa₂−a₁ = 3 · a₃−a₂ = 3 · a₄−a₃ = 3 → all equal
- 2ConclusionConstant difference → arithmetic sequence
- 3Extenda₅ = a₄ + d = 11 + 3 = 14, then 17, 20
- 4Evaluate aₙ for n = 10aₙ = 2 + (10 − 1)·3 = 29
First 12 terms
Most useful next
Formula
arithmetic: aₙ = a₁ + (n − 1)·d · geometric: aₙ = a₁·r^(n−1) · Fibonacci: aₙ = aₙ₋₁ + aₙ₋₂
Pro tips
- • Check differences first: equal differences → arithmetic. Then ratios: equal ratios → geometric.
- • Classic geometric examples: 1, 2, 4, 8 … (r = 2) or 100, 50, 25 … (r = ½).
- • Four terms are enough to confirm a simple linear or exponential rule.
FAQ
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