Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What characterizes a monotonic sequence?

It fluctuates between values
It is strictly increasing only
It is either non-increasing or non-decreasing
It has periodic values

The correct answer is: It is either non-increasing or non-decreasing

A monotonic sequence is characterized by consistently moving in one direction without fluctuation. This means that it is either non-increasing, which signifies that each term in the sequence is less than or equal to the one preceding it, or non-decreasing, indicating that each term is greater than or equal to the previous term. The key aspect is the absence of any increase and decrease at the same time; in simpler terms, the sequence does not "bounce around." Understanding the nature of a monotonic sequence helps in various areas of mathematics, particularly in calculus and analysis, where the behavior of sequences and functions is important. In contrast, sequences that fluctuate, are strictly increasing, or have periodic values do not meet the criteria for monotonicity, as they fail to maintain a consistent direction throughout their terms.