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Definition of Sequence Calculator

Online general-term calculator: given the linear term a_n=An+B, find the nth term; a sequence is a function on positive integers.

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a_n = A·n + B
Common difference A
First term A+B
Positive integer

📖 Tutorial | General Term

1. Definition
A sequence is an ordered list; the general term gives a_n as a function of n. This tool handles a_n=An+B.
2. Formula & Notation
a_nnth term
nIndex
3. Properties & Laws
  • a_n=An+B;
  • First term a_1=A+B;
  • Common difference A;
  • A function on positive integers.
4. Steps
  1. Enter A, B, n;
  2. Click "Find Term";
  3. Or click "Load Example".
5. Worked Examples
Example: a_n=2n+1 gives a_10=21.
6. Common Pitfalls
n starts at 1;
An+B is not A(n+B);
Mind the domain.

❓ FAQ | General Term

General term?
Relation to n.
First term?
A+B.
Linear?
An+B.
Vs function?
On positive integers.
n=0?
Starts at 1.
Arithmetic?
Difference A.
Uses?
Find terms, monotonicity.