Introduction to sequences

2010000403

Level:

We are given a sequence

{(5 n - 3)}_{n = 1}^{\infty}

. What does this formula express?

a sequence of all natural numbers which after dividing by

5

give the remainder

2

a sequence of all natural numbers which are divisible by

3

a sequence of all natural numbers which are divisible by

5

a sequence of all natural numbers which after dividing by

5

give the remainder

3

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

2010000401

Level:

We are given a sequence

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

. Which of the following formulations describes how is the given sequence defined?

defined by a formula for the

n

th term

defined by a list of the sequence elements

defined by a graph of the sequence

defined by a recursive formula for the sequence

1003084909

Level:

We were given an oscillating sequence

3, - 3, 3, - 3, 3 \dots

(numbers

3

and

- 3

alternate regularly). What is the formula for the

n

th element of the sequence?

a_{n} = (- 1)^{n + 1} \cdot 3, n \in N

a_{n} = (- 1)^{n} \cdot 3, n \in N

a_{n} = 3^{n}, n \in N

a_{n} = - 3^{n}, n \in N

1103084908

Level:

We were given a sequence

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

. Which of the diagrams shows correctly the first five elements of the sequence?

1003084907

Level:

A sequence

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

is defined by the relations:

a_{1} = 3; a_{n + 1} = \frac{a_{n}}{n + 2}, n \in N

. Which of the following descriptions is used to define the given sequence?

a recursion formula of a sequence

a formula of the

n

th term

a list of sequence elements

a graph of a sequence

1003084906

Level:

We are given a sequence

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

. Which of the following formulations describes how is the given sequence defined?

defined by a formula for the

n

th term

defined by a list of the sequence elements

defined by a graph of the sequence

defined by a recursive formula for the sequence

1103084905

Level:

Which sequence is defined by the given graph?

{(a_{n})}_{n = 1}^{5} = 2, 1, 3, 1, 2

{(a_{n})}_{n = 1}^{10} = 1, 2, 2, 1, 3, 3, 4, 1, 5, 2

{(a_{n})}_{n = 1}^{5} = 1, 2, 3, 4, 5

{(a_{n})}_{n = 1}^{5} = 1, 1, 2, 2, 3

1003084904

Level:

We were given a sequence

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

. Which expression describes the term

a_{n - 1} (n \in N; n > 1)

of the given sequence?

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

a_{n - 1} = n - 1

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

a_{n - 1} = \frac{1}{2 n - 1}

1003084903

Level:

The table contains ordered pairs of numbers

[n; a_{n}]

\begin{array}{cccccc} n & 1 & 2 & 3 & 4 & 5 \\ a_{n} & - 1 & 1 & - 2 & 2 & - 3 \end{array}

Which sequence is defined by the table?

{(a_{n})}_{n = 1}^{5} = - 1, 1, - 2, 2, - 3

{(a_{n})}_{n = 1}^{10} = 1, - 1, 2, 1, 3, - 2, 4, 2, 5, - 3

{(a_{n})}_{n = 1}^{5} = 1, 2, 3, 4, 5

{(a_{n})}_{n = 1}^{5} = 0, 3, 1, 6, 2

Introduction to sequences

2010000403

2010000402

2010000401

1003084909

1103084908

1003084907

1003084906

1103084905

1003084904

1003084903

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