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Recursive Sequence Calculator

Online recursive sequence calculator: given a_n=c·a_(n−1)+b and an initial value, iterate to the nth term and preview the terms.

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a_n=c·a_(n−1)+b
Starting term
c=1 arithmetic
b=0 geometric
Positive integer

📖 Tutorial | Recursion

1. Definition
A recursive sequence is given by a_n=c·a_(n−1)+b (n≥2) plus an initial value; this tool iterates term by term.
2. Formula & Notation
a₁Initial value
3. Properties & Laws
  • a_n=c·a_(n−1)+b;
  • Needs an initial value;
  • c=1 arithmetic, b=0 geometric;
  • Iteration matches the closed form.
4. Steps
  1. Enter a₁, c, b, n;
  2. Click "Find Term" to preview terms;
  3. Or click "Load Example".
5. Worked Examples
Example: a_n=2a_(n−1)+1 gives 1,3,7,15,31.
6. Common Pitfalls
Do not forget the initial value;
Recursion starts at n=2;
Do not swap c and b.

❓ FAQ | Recursion

Recursive?
Later from earlier terms.
How?
Iterate from a₁.
c=1?
Arithmetic.
b=0?
Geometric.
Initial value?
Essential.
Closed form?
See recurrence-to-general.
Consistent?
Yes.