Arithmetic sequences

1003047807

Level:

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?

$171\,\mathrm{cm}$

$2\,\mathrm{m}$

$180\,\mathrm{cm}$

$95\,\mathrm{cm}$

$123.5\,\mathrm{cm}$

1003047808

Level:

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 $80\ \mathrm{CZK}$?

$18\,720\ \mathrm{CZK}$

$624\ \mathrm{CZK}$

$4\,680\ \mathrm{CZK}$

$12\,480\ \mathrm{CZK}$

$6\,240\ \mathrm{CZK}$

1003107201

Level:

The sum of the first ten terms of an arithmetic sequence with odd subscripts is $190$, the sum of the first ten terms with even subscripts is $230$. Find the first term.

$-17$

$-34$

$5$

$4$

$10$

1003107202

Level:

The second term of an arithmetic sequence is $-21$, the fifth term is $21$. How many of the first consecutive terms do we have to add up to get a sum of more than $50$?

$8$

$7$

$6$

$9$

$5$

1003107203

Level:

Insert such $3$ numbers between the roots of the equation $x^2-10x-119=0$, so that together with the roots of the equation they form $5$ consecutive arithmetic sequence terms. What is the central term?

$5$

$17$

$6$

$-1$

$-7$

1003107204

Level:

Positive numbers which when divided by $3$ leave a remainder of $2$ are terms of an increasing arithmetic sequence. The sum of the first $15$ terms is $480$. Find the $3$rd term of this sequence.

$17$

$11$

$20$

$5$

$23$

1003107205

Level:

Sizes of angles in a triangle form three consecutive arithmetic sequence terms. The size of the largest angle is four times the smallest one. Find the size of the smallest angle of the triangle.

$24^{\circ}$

$30^{\circ}$

$60^{\circ}$

$20^{\circ}$

$35^{\circ}$

1003107206

Level:

Solve the equation with the variable $n$, where $n$ is a natural number: $$ 5+8+11+14+\dots+(3n+2)=735 $$

$21$

$65$

$20$

$68$

$10$

1003107207

Level:

Find the set of all solutions of the given inequality with the variable $x$, where $x$ is a natural number: $$ 5x+10x+15x+\dots+50x \leq 1000 $$

$ \{1;2;3\} $

$ \{ 2 \} $

$\{ 1;2;3;4;5\} $

$\{ 1 \}$

$\{1;2\}$

1003107208

Level:

Solve the equation with the variable $x$, where $x$ is a natural number: $$ \sum\limits_{n=1}^x(-3n+10)=-45 $$

$9$

$5$

$10$

$13$

$12$

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