Introduction to sequences

1003084902

Level:

We are given a sequence \( \left( 3n-2\right)^{\infty}_{n=1} \). What does this formula express?

a sequence of all natural numbers which after dividing by \( 3 \) give the remainder \( 1 \)

a sequence of all natural numbers which are divisible by \( 3 \)

a sequence of all natural numbers which are divisible by \( 2 \)

a sequence of all odd natural numbers

1003084901

Level:

We were given a sequence \( \left( 2n \right)^{\infty}_{n=1} \). What does this formula express?

a sequence of all even natural numbers

a sequence of all natural numbers

a sequence of all odd natural numbers

a sequence of all natural numbers that are divisible by \( 5 \)

1003107410

Level:

We were given a sequence \( \left(-n^2\right)_{n=1}^{\infty} \). This sequence is:

upper bounded

lower bounded

bounded

increasing

1003107409

Level:

We were given a sequence \( \left( 3+\frac1{2n}\right)_{n=1}^{\infty} \). This sequence is:

bounded

increasing

constant

non-decreasing

1003107408

Level:

A sequence \( \left(a_n\right)_{n=1}^{\infty} \) is defined recursively by: \( a_1=5;\ a_{n+1}=2a_n-1\text{, } n\in\mathbb{N} \). This sequence is:

lower bounded

upper bounded

bounded

decreasing

1003107407

Level:

We were given a sequence \( \left( \log n \right)_{n=1}^{\infty} \). This sequence is:

lower bounded

upper bounded

bounded

decreasing

1003107406

Level:

We were given a sequence \( \left( (-1)^n\cdot n\right)_{n=1}^{\infty} \). Complete the sentence: This sequence is ...

neither increasing nor decreasing.

increasing.

decreasing.

lower bounded.

1003107405

Level:

We were given a sequence \( \left( \log2^n\right)_{n=1}^{\infty} \). This sequence is:

increasing

decreasing

non-increasing

bounded

1003107404

Level:

We were given a sequence \( \left(2\cdot x^n\right)_{n=1}^{\infty} \). For what values of the parameter \( x \), \( x\in\mathbb{R} \), is the sequence increasing?

\( x\in(1;\infty) \)

\( x\in[1;\infty) \)

\( x\in(-\infty;1) \)

\( x\in(-\infty;1]\)

1003107403

Level:

We were given a sequence \( \left(\frac{n\cdot x}{n+1}\right)_{n=1}^{\infty} \). For what values of the parameter \( x \), \(x\in\mathbb{R}\), is the sequence decreasing?

\( x\in(-\infty; 0) \)

\( x\in(-\infty;0] \)

\( x\in(0;\infty) \)

\( x\in[0;\infty) \)

Introduction to sequences

1003084902

1003084901

1003107410

1003107409

1003107408

1003107407

1003107406

1003107405

1003107404

1003107403

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