arithmeticsequencesi · choose the number of players. for each player choose a face. single player...

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ARITHMETIC SEQUENCES I

JEOPARDY GAME

The goal is to gain maximum of the points by answering questions. The points forincorrect answers are subtracted. The game is designed either for a single player or

for two players (or two teams).

Created by P. Vondráková, P. Beremlijski, M. Litschmannová and R. Maříkfrom Department of Applied Mathematics, VŠB – Technical University of Ostrava.

Choose the number of players. For each player choose a face.

Single player Two players

1 1

Player 1Boy Girl

1

1

Player 2

Boy Girl

Two terms Three consecutivenumbers

More than threeconsecutivenumbers

One term anddifference

The game finished.The gameboard on the previous page allows to access the questions again.

THE WINNER IS

1111

11

NO WINEREQUAL SCORE

11

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Wonderfull. That’s right!Sorry, this is not right. NEXTTwo terms for 100.

Find the formula for the n-th term of an arithmetic sequence with the first term a1 = 1 and the secondterm a2 = −2.

A an = 1 − 2nan = −2 + nan = 4 − 3nan = 3 + 2n B an = 1 − 2nan = −2 + nan = 4 − 3nan = 3 + 2n

C an = 1 − 2nan = −2 + nan = 4 − 3nan = 3 + 2n D an = 1 − 2nan = −2 + nan = 4 − 3nan = 3 + 2n


In the arithmetic sequence given by the relations a1 = π, an+1 = an + 2π find a13.

A a13 = 27πa13 = 26πa13 = 25πa13 = 24π B a13 = 27πa13 = 26πa13 = 25πa13 = 24π

C a13 = 27πa13 = 26πa13 = 25πa13 = 24π D a13 = 27πa13 = 26πa13 = 25πa13 = 24π


The arithmetic sequence is defined by the first term a1 = 17 and the fifth term a5 = 11. Find the termwhich is seven times smaller than the third term of the sequence.

A a2a8a11a17a21 B a2a8a11a17a21 C a2a8a11a17a21 D a2a8a11a17a21 E a2a8a11a17a21

Wonderfull. That’s right!Sorry, this is not right. NEXTThree consecutive numbers for 100.

The following numbers form an arithmetic sequence. Find x.

1 , x , 3

A x = 2x = −2x = 2.5x = 1.5 B x = 2x = −2x = 2.5x = 1.5

C x = 2x = −2x = 2.5x = 1.5 D x = 2x = −2x = 2.5x = 1.5



x , 10 , 5

A x = 15x = 20x = 50x = 5 B x = 15x = 20x = 50x = 5

C x = 15x = 20x = 50x = 5 D x = 15x = 20x = 50x = 5


Identify the real number x which ensures that the numbers a1 = x2 + 10, a2 = x2 + 2x and a3 = x2

are three consecutive terms of an arithmetic sequence.

A x = 0x = 2x = 2.5x = 5x = −5 B x = 0x = 2x = 2.5x = 5x = −5 C x = 0x = 2x = 2.5x = 5x = −5 D x = 0x = 2x = 2.5x = 5x = −5 E x = 0x = 2x = 2.5x = 5x = −5

Wonderfull. That’s right!Sorry, this is not right. NEXTMore than three consecutive numbers for 100.


4 , a , 8 , b , x

A x = 12x = 10x = 14x = 16 B x = 12x = 10x = 14x = 16

C x = 12x = 10x = 14x = 16 D x = 12x = 10x = 14x = 16



5 , a , b , x , 6

A x = 5.75x = 5.5x = 5.8x = 523

B x = 5.75x = 5.5x = 5.8x = 523

C x = 5.75x = 5.5x = 5.8x = 523

D x = 5.75x = 5.5x = 5.8x = 523



x , 1 , a , b , c , d , 0.5

A x = 1.1x = 1.5x = −0.5x = 2 B x = 1.1x = 1.5x = −0.5x = 2

C x = 1.1x = 1.5x = −0.5x = 2 D x = 1.1x = 1.5x = −0.5x = 2

Wonderfull. That’s right!Sorry, this is not right. NEXTOne term and difference for 100.

Find the recurrence equations for the arithmetic sequence with the first term a1 = 4 and the differenced = −2.

A a1 = 4; an+1 = an − 2a1 = 4; an+1 = a1 − 2an = 4 + an+2an+1 = an + 2 B a1 = 4; an+1 = an − 2a1 = 4; an+1 = a1 − 2an = 4 + an+2an+1 = an + 2

C a1 = 4; an+1 = an − 2a1 = 4; an+1 = a1 − 2an = 4 + an+2an+1 = an + 2 D a1 = 4; an+1 = an − 2a1 = 4; an+1 = a1 − 2an = 4 + an+2an+1 = an + 2


Find the first term a1 and the difference d of the arithmetic sequence (5 + 2n)∞n=1.

A a1 = 5; d = 2a1 = 3; d = −2a1 = 2; d = 5a1 = 7; d = 2 B a1 = 5; d = 2a1 = 3; d = −2a1 = 2; d = 5a1 = 7; d = 2

C a1 = 5; d = 2a1 = 3; d = −2a1 = 2; d = 5a1 = 7; d = 2 D a1 = 5; d = 2a1 = 3; d = −2a1 = 2; d = 5a1 = 7; d = 2


The arithmetic sequence is given by the third term a3 = 5 and the difference d = 2. How many termsof the sequence has to be summed up to ensure that the sum is bigger than 300?

A 1012141618 B 1012141618 C 1012141618 D 1012141618 E 1012141618

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arithmeticsequencesi · choose the number of players. for each player choose a face. single player...

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