9000072707
Level:
B
We are given seven consecutive terms of an arithmetic sequence. Find
\(x\).
\[
100\, ,\ a\, ,\ b\, ,\ x\, ,\ c\, ,\ d\, ,\ 0
\]
\(x = 50\)
\(x = 60\)
\(x = 40\)
\(x = 51\)
Arithmetic sequences
9000072708
Level:
B
We are given six consecutive terms of an arithmetic sequence. Find
\(x\).
\[
\frac52,\ a,\ x,\ b,\ c,\ 5
\]
\(x = 3.5\)
\(x = 3\)
\(x = 4\)
\(x = 3.75\)
9000072709
Level:
B
We are given seven consecutive terms of an arithmetic sequence. Find
\(x\).
\[
x,\ 1,\ a,\ b,\ c,\ d,\ \frac12
\]
\(x = 1.1\)
\(x = 1.5\)
\(x = -0.5\)
\(x = 2\)
9000072710
Level:
B
We are given seven consecutive terms of an arithmetic sequence. Find
\(x\).
\[
\frac{4}
{5}\, ,\ a\, ,\ b\, ,\ 0\, ,\ c\, ,\ d\, ,\ x
\]
\(x = -\frac{4}
{5}\)
\(x = \frac{5}
{4}\)
\(x = -\frac{5}
{4}\)
\(x = -\frac{8}
{5}\)
1003047801
Level:
C
A certain type of bamboo grows $1.3\,\mathrm{m}$ per day during the vegetation period. Concerning the fact that it reached a height of $30\,\mathrm{m}$ after twenty days of regular growth, how tall was it at the beginning of the first day?
$4\,\mathrm{m}$
$5.3\,\mathrm{m}$
$2.7\,\mathrm{m}$
$10\,\mathrm{m}$
$4.3\,\mathrm{m}$
1003047802
Level:
C
A student solves several math problems every day. How many problems will he solve in $14$ days if he manages to solve $5$ on the first day and then gradually increases the number of problems solved by $2$ a day?
$252$
$140$
$434$
$364$
$70$
1003047803
Level:
C
In Duolingo application, every user earns so-called lingots (=virtual currency), providing he or she learns at least $10$ minutes for $10$ consecutive days. For the first $10$ days a user earns $1$ lingot, $2$ lingots for the next ten-day period, $3$ lingots for the following $10$ days (i.e. for the first $30$ days a user earns $6$ lingots), etc. Find the smallest number of days in which a user can accumulate $1000$ lingots.
$450$
$45$
$440$
$44$
$430$
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).
$18$
$22$
$32$
$15$
$20$
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?
$6\,\mathrm{km}$
$7\,\mathrm{km}$
$5\,\mathrm{km}$
$4\,\mathrm{km}$
$3\,\mathrm{km}$
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 ($n$).
$c=\frac n2(21-n)$
$c=10-\frac{n^2}2$
$c=\frac{11n}2$
$c=\frac n2(10+10n)$
$c=\frac n2(11-n)$