Question 1

Which of the following is an example of a monotonic sequence that is bounded and convergent?

Accepted Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Question 2

Which sequence is an example of a monotonic decreasing and bounded sequence?

Accepted Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Question 3

Which of the following conditions guarantees that a sequence is monotonic?

Accepted Answer

The differences between consecutive terms are consistently positive or negative.

Answer

The terms alternate between positive and negative.

Answer

The terms of the sequence are random.

Answer

The sequence converges to a limit.

Question 4

For a sequence to be considered monotonically decreasing, which of the following must be true?

Accepted Answer

Each term in the sequence is less than or equal to the preceding term.

Answer

The sequence terms remain constant.

Answer

Each term in the sequence is greater than or equal to the preceding term.

Answer

The sequence terms oscillate between positive and negative values.

Question 5

Which of the following sequences is divergent but monotonic?

Accepted Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Question 6

Which of the following sequences is not monotonic?

Accepted Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Question 7

Which sequence is an example of a monotonic increasing sequence?

Accepted Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Question 8

Which of the following sequences is an example of a monotonic decreasing sequence?

Accepted Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Answer

a_n = \frac{1}{n}

Question 9

Which property does a strictly decreasing sequence always possess?

Accepted Answer

Each term is smaller than the previous one

Answer

All terms are identical

Answer

It converges to zero

Answer

It is unbounded above

Question 10

Which of the following sequences is an example of a monotonic sequence?

Accepted Answer

a_n = 5 - n

Answer

a_n = sin(n)

Answer

a_n = n^(-1) * (-1)^n

Answer

a_n = (-1)^n * n

Question 11

Which of the following sequences is bounded both above and below?

Accepted Answer

The sequence $ a_n = (-1)^n $

Answer

The sequence $ a_n = n^2 $

Answer

The sequence $ a_n = \frac{1}{n} $

Answer

The sequence $ a_n = n $

Question 12

Which of the following statements is true regarding bounded sequences?

Accepted Answer

A bounded sequence converges to a limit if it is also monotonic.

Answer

Bounded sequences cannot diverge.

Answer

A bounded sequence must be periodic.

Answer

All bounded sequences are convergent.

Question 13

Which of the following sequences is an example of a decreasing sequence?

Accepted Answer

a_n = 10 - n

Answer

a_n = n^2

Answer

a_n = 2^n

Answer

a_n = 5n + 3

Question 14

Which sequence is neither increasing nor decreasing?

Accepted Answer

a_n = (-1)^n

Answer

a_n = e^n

Answer

a_n = \frac{1}{n}

Answer

a_n = n^3

Question 15

Which of the following sequences is strictly increasing?

Accepted Answer

a_n = 4n

Answer

a_n = 7 - n

Answer

a_n = -2n

Answer

a_n = 10 - 3n

Question 16

Consider the sequence $ a_n = \frac{1}{n} $ for $ n \geq 1 $. Which statement is correct about this sequence?

Accepted Answer

The sequence is strictly decreasing.

Answer

The sequence is constant.

Answer

The sequence is neither increasing nor decreasing.

Answer

The sequence is strictly increasing.

Question 17

Which of the following sequences is constant?

Accepted Answer

a_n = 5

Answer

a_n = n^2

Answer

a_n = n - 7

Answer

a_n = 2n + 3

Question 18

What type of sequence is defined by $ a_n = 2^n $ for $ n \geq 0 $?

Accepted Answer

The sequence is strictly increasing.

Answer

The sequence oscillates.

Answer

The sequence is constant.

Answer

The sequence is strictly decreasing.

Question 19

Which of the following sequences is described as strictly decreasing?

Accepted Answer

a_n = 100 - n

Answer

a_n = n + 5

Answer

a_n = 3^n

Answer

a_n = 2n

Question 20

Given the sequence $ b_n = \frac{n}{n+1} $, which of the following statements is true?

Accepted Answer

The sequence is strictly increasing.

Answer

The sequence is constant.

Answer

The sequence oscillates.

Answer

The sequence is strictly decreasing.

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