2010000207
Level:
B
The picture shows a part of the graph of the arithmetic sequence. Find the sum of the first twenty-five terms of the sequence.
\( -350\)
\( -32\)
\( -68\)
\( -800\)
B
2010000206
Level:
B
Find the third term of an arithmetic sequence \( (a_n)^{\infty}_{n=1}\), if the sum of the first \(n\) terms is equal to \(2n^2+3n\).
\( a_3 = 13\)
\( a_3 = 27\)
\( a_3 = 23\)
\( a_3 = 46\)
2010000205
Level:
B
Find the third term of an arithmetic sequence \( (a_n)^{\infty}_{n=1}\), if the sum of the first \(n\) terms is equal to \(4n^2-3n\).
\( a_3 = 17\)
\( a_3 = 27\)
\( a_3 = 19\)
\( a_3 = 38\)
2010000202
Level:
B
The \( 5 \)th term of an arithmetic sequence is \( -100 \) and the common difference is \( 4 \). Choose the correct statement about the sum of the first \( 50 \) terms.
\( s_{50} = -900 \)
\( s_{50} < -900 \)
\( s_{50} < 0 \) and \( s_{50} > -900 \)
\( s_{50} > 0 \) and \( s_{50} < 900 \)
\( s_{50} > 900 \)
2010000201
Level:
B
The sum of the first \( 27 \) terms of an arithmetic sequence is \( 1242 \) and the first term is \( 7\). Choose the incorrect statement about its common difference.
\( d \) is an even number
\( d < 4 \)
\( d > 0 \)
\( d \) is a prime number
2010001003
Level:
B
The arithmetic sequence is defined by the first term
\(a_{1} = 15\) and the
fourth term \(a_{4} = 13\).
Find the term which is three times smaller than the tenth term of the sequence.
\( a_{19}\)
\( a_{9}\)
\( a_{7}\)
\( a_{14}\)
\( a_{12}\)
2000003001
Level:
B
Which of the given numbers is the solution of the equation
\( 3^{2x} + \frac{4}{27} = 2\cdot 3^{2x+1}-9^x\)?
\( x=-\frac{3}{2} \)
\( x=1 \)
\( x=\frac{3}{2} \)
\( x=-1\)
2000002905
Level:
B
Determine all the natural numbers that are solutions of the inequality:
\[
-\frac{9}{8} \leq -\frac{x}{4}
\]
\( x \in \{ 1;2;3;4\} \)
\( x \in \mathbb{N} \)
\( x \in \{0; 1;2;3;4\} \)
\( x \in \{ 1;2;3;4;5\} \)
2000002904
Level:
B
Determine the largest integer that is the solution of the inequality:
\[
-1.2x > -1.44
\]
\( 1\)
\( 2 \)
\( 0 \)
\( -1\)
2000002903
Level:
B
Determine the largest integer that is the solution of the inequality:
\[
-0.16x > 6.4
\]
\( -41\)
\( -39 \)
\( -40\)
\( -42\)