Monotonicity of sequences
Types of exercises: monotonicity of a sequence, the difference of consecutive terms of a sequence, monotonicity of a recursively defined sequence.
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To determine the monotonicity of the sequence (aₙ), one computes the difference aₙ₊₁ − aₙ. Choose the expression equal to this difference for every n ≥ 1
aₙ = −3n² − n − 9
The sequence (aₙ) is defined recursively for n ≥ 1. Determine whether it is increasing, decreasing, constant or not monotonic
a₁ = −5, aₙ₊₁ = −3aₙ
Determine whether the sequence is increasing, decreasing, constant or not monotonic
aₙ = −2n² + n
To determine the monotonicity of the sequence (aₙ), one computes the difference aₙ₊₁ − aₙ. Choose the expression equal to this difference for every n ≥ 1
aₙ = −3n² + 3n − 7
The sequence (aₙ) is defined recursively for n ≥ 1. Determine whether it is increasing, decreasing, constant or not monotonic
a₁ = −2, aₙ₊₁ = aₙ + 3n + 2
Determine whether the sequence is increasing, decreasing, constant or not monotonic
aₙ = −2n² − 3n + 9
To determine the monotonicity of the sequence (aₙ), one computes the difference aₙ₊₁ − aₙ. Choose the expression equal to this difference for every n ≥ 1
aₙ = 3n² + 2n + 3
The sequence (aₙ) is defined recursively for n ≥ 1. Determine whether it is increasing, decreasing, constant or not monotonic
a₁ = −8, aₙ₊₁ = aₙ + 2n − 9
Determine whether the sequence is increasing, decreasing, constant or not monotonic
aₙ = −1
To determine the monotonicity of the sequence (aₙ), one computes the difference aₙ₊₁ − aₙ. Choose the expression equal to this difference for every n ≥ 1
aₙ = 3n² + 4n − 7
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