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Which of the following is NOT a monotone sequence?*1 point{1, 3/2, 2, 5/2, 3, ...}{20, 19, 10, 8, 5, 2, 1, 1}{1/2, 2/3, 3/4, 4/5, 5/6, ....}{-1/2, 2/3, -3/4, 4/5, -5/6, ....}

Question

Which of the following is NOT a monotone sequence?*1 point{1, 3/2, 2, 5/2, 3, ...}{20, 19, 10, 8, 5, 2, 1, 1}{1/2, 2/3, 3/4, 4/5, 5/6, ....}{-1/2, 2/3, -3/4, 4/5, -5/6, ....}

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Solution

The sequence that is NOT a monotone sequence is {20, 19, 10, 8, 5, 2, 1, 1}.

A monotone sequence is a sequence that is either entirely non-increasing or non-decreasing.

Let's check each sequence:

  1. {1, 3/2, 2, 5/2, 3, ...} is a monotone increasing sequence because each term is larger than the one before it.

  2. {20, 19, 10, 8, 5, 2, 1, 1} is not a monotone sequence because it decreases from 20 to 19, but then jumps down to 10, which is not a consistent decrease.

  3. {1/2, 2/3, 3/4, 4/5, 5/6, ....} is a monotone increasing sequence because each term is larger than the one before it.

  4. {-1/2, 2/3, -3/4, 4/5, -5/6, ....} is not a monotone sequence because it alternates between positive and negative values. However, if we ignore the signs, the absolute values of the terms form a monotone increasing sequence.

So, the sequence {20, 19, 10, 8, 5, 2, 1, 1} is the one that is NOT a monotone sequence.

This problem has been solved

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