Lesson 72 of 1524
Sequences, Probability, and Counting Theory
Explicit formulas define each term of a sequence using the position of the term
Practice this chapterExplicit formulas define each term of a sequence using the position of the term An explicit formula for the n th term of a sequence can be written by analyzing the pattern of several terms
Recursive formulas define each term of a sequence using previous terms Recursive formulas must state the initial term, or terms, of a sequence
sequence — a function whose domain is a subset of the positive integers. probability — a number from 0 to 1 indicating the likelihood of an event. explicit formula — a formula that defines each term of a sequence in terms of its position in the sequence. recursive formula — a formula that defines each term of a sequence using previous term(s).
Worked example
What does “sequence” mean in Sequences, Probability, and Counting Theory?
- 1Use the wording this chapter gives for sequence.
- 2The book says: a function whose domain is a subset of the positive integers.
- 3Do not use the meaning of probability. That term means a number from 0 to 1 indicating the likelihood of an event.
Result: a function whose domain is a subset of the positive integers
Why. That is the meaning this chapter gives for sequence.
Do not swap sequence and probability. sequence means a function whose domain is a subset of the positive integers. probability means a number from 0 to 1 indicating the likelihood of an event.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.