2010000602
Level:
A
Given the sets \(A = [ -8;3 ]\) and \(B =(0;10)\) find the set difference \(A \setminus B\).
\( [ -8;0 ] \)
\( [ -8;0 )\)
\( ( 0;10)\)
\( ( 0;3 ]\)
A
2010000406
Level:
A
We are given a sequence \( \left( a_n \right)^{5}_{n=1}\) defined by the following graph. Find the formula of the \(n\)th term of this sequence.
\( a_n = 2n-3,\ n \in\{1,\ \ 2,\ \ 3,\ \ 4,\ \ 5 \}\)
\( a_n = 2n,\ n \in\{1,\ \ 2,\ \ 3,\ \ 4,\ \ 5 \}\)
\( a_n = 3-2n,\ n \in\{1,\ \ 2,\ \ 3,\ \ 4,\ \ 5 \}\)
\( a_n = 2n-1,\ n \in\{1,\ \ 2,\ \ 3,\ \ 4,\ \ 5 \}\)
2010000405
Level:
A
We are given a sequence \( \left( a_n \right)^{5}_{n=1}\) defined by the following graph. Find the formula of the \(n\)th term of this sequence.
\( a_n = 3-2n,\ n \in\{1,\ \ 2,\ \ 3,\ \ 4,\ \ 5 \}\)
\( a_n = 2n,\ n\in\{1,\ \ 2,\ \ 3,\ \ 4,\ \ 5 \}\)
\( a_n = 1-2n,\ n\in\{1,\ \ 2,\ \ 3,\ \ 4,\ \ 5 \}\)
\( a_n = 2n-3,\ n\in\{1,\ \ 2,\ \ 3,\ \ 4,\ \ 5 \}\)
2010000404
Level:
A
Which sequence is defined by the given graph?
\( \left( a_n \right)^{5}_{n=1} = 3,\ \ 2,\ \ 1,\ \ 2,\ \ 3 \)
\( \left( a_n \right)^{10}_{n=1} = 1,\ \ 3,\ \ 2,\ \ 2,\ \ 3,\ \ 1,\ \ 4,\ \ 2,\ \ 5,\ \ 3 \)
\( \left( a_n \right)^{5}_{n=1} = 1,\ \ 2,\ \ 3,\ \ 4,\ \ 5 \)
\( \left( a_n \right)^{5}_{n=1} = 1,\ \ 2,\ \ 2,\ \ 3,\ \ 3 \)
2010000403
Level:
A
We are given a sequence \( \left( 5n-3\right)^{\infty}_{n=1} \).
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 \(3\)
2010000401
Level:
A
We are given a sequence \( \left( \frac{n}{n+1} \right)_{n=1}^{\infty} \).
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
2010000204
Level:
A
Insert five numbers between \(3\) and \(33\) such that the resulting sequence is a part of an arithmetic sequence and find the common difference \(d\).
\( d=5\)
\( d=6\)
\( d=-5\)
\( d=\frac{30}{7}\)
2010000203
Level:
A
Insert five numbers between \(15\) and \(57\) such that the resulting sequence is a part of an arithmetic sequence and find the common difference \(d\).
\( d=7\)
\( d=6\)
\( d=12\)
\( d=-7\)
2010001005
Level:
A
The picture shows a part of the graph of the arithmetic sequence. What is the twenty-third term?
\( -53\)
\(-56\)
\(-62\)
\(-23\)
2010001004
Level:
A
The picture shows a part of the graph of the arithmetic sequence. What is the thirty-second term?
\( 143\)
\(148\)
\( 32\)
\( 158\)