2010001005
Level:
A
The picture shows a part of the graph of the arithmetic sequence. What is the twenty-third term?
\( -53\)
\(-56\)
\(-62\)
\(-23\)
Arithmetic sequences
2010001004
Level:
A
The picture shows a part of the graph of the arithmetic sequence. What is the thirty-second term?
\( 143\)
\(148\)
\( 32\)
\( 158\)
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.
\( a_{19}\)
\( a_{9}\)
\( a_{7}\)
\( a_{14}\)
\( a_{12}\)
2010001002
Level:
A
Given an arithmetic sequence $(a_n)_{n=1}^{\infty}$, where $a_5=\frac54$, $a_k=15$ and the common difference is $\frac{11}{4}$, find $k$.
\(10\)
\(-6\)
\(0\)
\(9\)
\( 6\)
2010001001
Level:
A
The \( n \)th term of an arithmetic sequence is \( -70 \), the common difference is \( -6 \) and the first term is \(2\). Find the \(n\).
\( 13\)
\(11\)
\(-11\)
\(-13\)
\(12\)
1003047808
Level:
C
A heavy smoker decides to reduce his daily consumption by $2$ cigarettes for $30$ days from the beginning of the next year. Then reduces his consumption again by $2$ cigarettes per day every $30$ days. How much will he save in $360$ days, given that one box of cigarettes ($20$ cigarettes) costs $80\ \mathrm{CZK}$?
$18\,720\ \mathrm{CZK}$
$624\ \mathrm{CZK}$
$4\,680\ \mathrm{CZK}$
$12\,480\ \mathrm{CZK}$
$6\,240\ \mathrm{CZK}$
1003047807
Level:
C
At a dorm, students play with rolls of toilet paper, building a pyramid of it. There is one roll at the top of the pyramid, in each lower row there is one roll more than in the one above it. How high will the pyramid be, given the fact that they have a total of $171$ rolls and one roll is $9.5\,\mathrm{cm}$ high?
$171\,\mathrm{cm}$
$2\,\mathrm{m}$
$180\,\mathrm{cm}$
$95\,\mathrm{cm}$
$123.5\,\mathrm{cm}$
1003047806
Level:
C
Every school must pay a registration fee for each participant it sends to a math competition. The fee for the first participant is $10$ euros, for each additional one the fee is one euro less. The maximum number of participants any school can register is $10$. Find the relationship between the price ($c$) paid by the school and the number of students registered ($n$).
$c=\frac n2(21-n)$
$c=10-\frac{n^2}2$
$c=\frac{11n}2$
$c=\frac n2(10+10n)$
$c=\frac n2(11-n)$
1003047805
Level:
C
A cyclist plans to travel $1666\,\mathrm{km}$ in $14$ days during her vacation. She knows that the number of kilometers she rides every day will decrease by the same number so she planned her route accordingly. At the beginning of the last day she was only $80\,\mathrm{km}$ away from her goal. What is the difference between the numbers of kilometers she rode on two consecutive days?
$6\,\mathrm{km}$
$7\,\mathrm{km}$
$5\,\mathrm{km}$
$4\,\mathrm{km}$
$3\,\mathrm{km}$
1003047804
Level:
C
The pianist wanted to learn a new composition in $3$ weeks ($21$ days). He decided to learn the same number of bars (measures) a day. In the end, however, he met his plan only on the first day. Every other day, he managed to learn by one bar fewer than the previous day. Find how many bars did he learn on the $15$th day knowing that he was able to learn a total of $462$ measures (in $21$ days).
$18$
$22$
$32$
$15$
$20$