notes/education/math/MATH1220 (calc II)/Sequences.md

A sequence is defined as an ordered list of numbers.

• Sequences are ordered, meaning two sequences that contain the same values but in a different order are not equal.
• Sequences can be infinite if a rule is defined, i.e \{1, 1, 1, 1, ...\}; a_i = 1

Behavior

• A sequence is considered increasing if a_n is smaller than a_{n+1} for all n.

• A sequence is considered decreasing if a_n is greater than or equal to a_{n+1} for all n.

• Sequences exist that do not fall into either category, i.e, a_n = (-1)^n

• If the terms of a sequence grow \{a_n\} get arbitrarily close to a single number L as n grows larger, this is noted by writing: $