Recursive Sequence Calculator
Generate terms from aₙ = r·aₙ₋₁ + d, including Fibonacci-style rules.
Enter your values
ⓘ Live results
Results
- nth term
- 301.546875
- First terms
- 2, 6, 12, 21, 34.5, 54.75, 85.125, 130.688, 199.031, 301.547
- Sum of all terms
- 846.640625
- Long-run limit
- Diverges (|r| ≥ 1)
- Behaviour
- Growing without bound
Quick answer
A linear recurrence aₙ = r·aₙ₋₁ + d builds each term from the last; it converges to d ÷ (1 − r) when |r| < 1.
aₙ = r·aₙ₋₁ + d
How to use the Recursive Sequence Calculator
- 1Enter the starting term.
- 2Enter the multiplier and the constant added each step.
- 3Set how many terms you want listed — the nth term and running total appear instantly.
Worked example
Using the values the calculator loads with:
Inputs
- First term a₁2
- Multiplier r1.5
- Added constant d3
- Terms to generate10
Results
- nth term301.546875
- First terms2, 6, 12, 21, 34.5, 54.75, 85.125, 130.688, 199.031, 301.547
- Sum of all terms846.640625
- Long-run limitDiverges (|r| ≥ 1)
- BehaviourGrowing without bound
Frequently asked questions
Can it do Fibonacci?
Fibonacci needs the two previous terms, so it is a second-order recurrence. This tool covers first-order rules of the form aₙ = r·aₙ₋₁ + d.
What is the fixed point?
The value where the sequence stops changing: d ÷ (1 − r), which the sequence approaches when |r| < 1.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.