Sequences are ordered lists of elements where the position of each element is significant. They can be finite or infinite and often follow a specific pattern or rule.
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The position of each term in a sequence is known as its index.
An arithmetic sequence has a constant difference between consecutive terms.
A geometric sequence has a constant ratio between consecutive terms.
Sequences can be represented using set notation when considering them as subsets within a universal set.
Review Questions
What distinguishes an arithmetic sequence from a geometric sequence?
How would you describe the n-th term in a general sequence?
Can sequences be considered subsets, and if so, how?
Related terms
Subset: A subset is a set containing some or all elements of another set.
Arithmetic Sequence: An arithmetic sequence is a sequence in which the difference between consecutive terms remains constant.
Geometric Sequence: A geometric sequence is one where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.