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 cm

high?

171 cm

2 m

180 cm

95 cm

123.5 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 CZK

18 720 CZK

624 CZK

4 680 CZK

12 480 CZK

6 240 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} - 10 x - 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 + (3 n + 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:

5 x + 10 x + 15 x + \dots + 50 x \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_{n = 1}^{x} (- 3 n + 10) = - 45

9

5

10

13

12

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