ARITHMETICSEQUENCESI · Choose the number of players. For each player choose a face. Single player...
Transcript of 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
Wonderfull. That’s right!Sorry, this is not right. NEXTTwo terms for 200.
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
Wonderfull. That’s right!Sorry, this is not right. NEXTTwo terms for 300.
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
Wonderfull. That’s right!Sorry, this is not right. NEXTThree consecutive numbers for 200.
The following numbers form an arithmetic sequence. Find x.
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
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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.
The following numbers form an arithmetic sequence. Find x.
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
Wonderfull. That’s right!Sorry, this is not right. NEXTMore than three consecutive numbers for 200.
The following numbers form an arithmetic sequence. Find x.
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
Wonderfull. That’s right!Sorry, this is not right. NEXTMore than three consecutive numbers for 300.
The following numbers form an arithmetic sequence. Find x.
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
Wonderfull. That’s right!Sorry, this is not right. NEXTOne term and difference for 200.
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
Wonderfull. That’s right!Sorry, this is not right. NEXTOne term and difference for 300.
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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