Introduction to sequences

1003107404

Level:

We were given a sequence

{(2 \cdot x^{n})}_{n = 1}^{\infty}

. For what values of the parameter

x

x \in R

, is the sequence increasing?

x \in (1; \infty)

x \in [1; \infty)

x \in (- \infty; 1)

x \in (- \infty; 1]

1003107405

Level:

We were given a sequence

{(\log 2^{n})}_{n = 1}^{\infty}

. This sequence is:

increasing

decreasing

non-increasing

bounded

1003107406

Level:

We were given a sequence

{((- 1)^{n} \cdot n)}_{n = 1}^{\infty}

. Complete the sentence: This sequence is ...

neither increasing nor decreasing.

increasing.

decreasing.

lower bounded.

1003107407

Level:

We were given a sequence

{(\log n)}_{n = 1}^{\infty}

. This sequence is:

lower bounded

upper bounded

bounded

decreasing

1003107408

Level:

A sequence

{(a_{n})}_{n = 1}^{\infty}

is defined recursively by:

a_{1} = 5; a_{n + 1} = 2 a_{n} - 1, n \in N

. This sequence is:

lower bounded

upper bounded

bounded

decreasing

1003107409

Level:

We were given a sequence

{(3 + \frac{1}{2 n})}_{n = 1}^{\infty}

. This sequence is:

bounded

increasing

constant

non-decreasing

1003107410

Level:

We were given a sequence

{(- n^{2})}_{n = 1}^{\infty}

. This sequence is:

upper bounded

lower bounded

bounded

increasing

2000010307

Level:

Which of the following sequences given by the recursive formulas is not decreasing?

a_{n + 1} = \frac{1}{a_{n}}

a_{1} = 5

a_{n + 1} = \sqrt{a_{n}}

a_{1} = 16

a_{n + 1} = 0.5 \cdot a_{n}

a_{1} = 12

a_{n + 1} = \frac{a_{n}}{n}

a_{1} = 24

2010000402

Level:

We are given the sequence

{(\frac{n}{n + 1})}_{n = 1}^{\infty}

. Find the recursive formula of such sequence.

a_{1} = \frac{1}{2}; a_{n + 1} = a_{n} \frac{(n + 1)^{2}}{n (n + 2)}, n \in N

a_{1} = 2; a_{n + 1} = a_{n} \frac{(n + 1)^{2}}{n (n + 2)}, n \in N

a_{1} = \frac{1}{2}; a_{n + 1} = a_{n} \frac{n (n + 1)}{(n + 1) (n + 2)}, n \in N

a_{1} = 2; a_{n + 1} = a_{n} \frac{n (n + 1)}{(n + 1) (n + 2)}, n \in N

2010000701

Level:

We are given the sequence

{(a n + b)}_{n = 1}^{\infty}

. This sequence satisfies

a_{7} - a_{2} = - 10

. Use this information to find

a

a = - 2

a = 2

a = - 1

a = 1

Introduction to sequences

1003107404

1003107405

1003107406

1003107407

1003107408

1003107409

1003107410

2000010307

2010000402

2010000701

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