Constant sequence
Definition
A constant sequence is a sequence in which every term is the same. This means that for any index 'n,' the value of the nth term is equal to some constant 'c.'
5 Must Know Facts For Your Next Test
- In a constant sequence, all terms are identical.
- The formula for a constant sequence can be written as a_n = c, where c is a fixed number.
- A constant sequence converges to the constant value itself.
- Constant sequences are considered arithmetic sequences with a common difference of zero.
- Every constant sequence is also a geometric sequence with a common ratio of one.
Review Questions
- What is the general form of the nth term in a constant sequence?
- Can a constant sequence be classified as both an arithmetic and geometric sequence? Explain why or why not.
- What does it mean for a constant sequence to converge?
"Constant sequence" appears in:
Related terms
Arithmetic Sequence: A sequence of numbers in which the difference between consecutive terms is always the same.
Geometric Sequence: A sequence where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Convergence: The property of approaching a specific value as more terms are added in a sequence.
