Karteikarten: Understanding Numerical Sequences and Monotonicity — 12 Karten

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.