Sequence — definition?
Ordered list of numbers with a specific rule.
General term — notation?
Denoted by Um, indicates position m.
Explicit sequence — role?
Directly defines Um as a function of m.
Recursive sequence — role?
Defines each term from the previous one.
Next term calculation — explicit?
Substitute m+1 into explicit formula.
Next term calculation — recursive?
Use recurrence relation from current term.
Graphical sequence — representation?
Points (m, Um) as a point cloud.
Monotonicity — meaning?
Sequence consistently increasing or decreasing.
Increasing sequence — condition?
Difference Um+1 - Um > 0.
Decreasing sequence — condition?
Difference Um+1 - Um < 0.
Powers and fractions — monotonicity?
Sequences like 3^m or m/(m+1) are increasing.
Difference — significance?
Determines if sequence is increasing or decreasing.
Test your knowledge with 6 questions on Understanding Numerical Sequences and Monotonicity.
1. What is the role of the general term symbol Um in the notation of a numerical sequence?
2. How would you calculate the 5th term of a sequence given an explicit definition Um = 3m + 2?
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