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denis23 [38]
3 years ago
5

Ronnie is scheduling a chess tournament in which each player plays every other player once. He created a table and found that ea

ch new player adds more games to the tournament in an arithmetic sequence. Answer this set of project questions regarding the chess games.
table:
# of players | # of games
1 | 0
2 | 1
3 | 3
4 | 6
5 | 10
Which of the following is a recursive rule for the original sequence?
A) an = an-1 + n + 1
B) an = an-1 + n - 1
C) an = an-1 + n
D) an = n2+ n

How many games must be played when 7 players are in the tournament?
Mathematics
1 answer:
aalyn [17]3 years ago
3 0
1) According to the table represented above, the number of games that can be played when 7 players are in the tournament is definitely 21 games. As you can see, in the last row there are 4 players to 5,which means that we have 4 new games. The same happens if we go from 3 players to 4, and finelly we have 3.
<span>
2) And what about the </span>recursive rule for the original sequence, the approrpiate one is <span>an = an-1 + n - 1, so the answer is lying in the second option from the scale.
</span>According to the fact that the number of games is actually the sum of integers from 1 to n-1 we expect to have n number of players.
<span>I am sure it's clear now!

</span>
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What is 0.00837 written in scientific notation?
Angelina_Jolie [31]

Answer:

8.37 x 10^-3

(Scientific Notation)

 

8.37 x 10^-3

(use the caret symbol [^] to type or write)

8.37E-3

(Scientific E-notation)

0.00837

(Real Number)

Step-by-step explanation:

How to convert numbers or decimals to scientific notation?

In scientific notation all numbers are written in the form of m×10n (m times ten raised to the power of n), where the exponent n is an integer, and the coefficient m is any real number, called the significand or mantissa. If the number is negative then a minus sign precedes m (as in ordinary decimal notation).

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Get the general term for the sequence being your t3 = 11 and the t20 = 244.2
marusya05 [52]

Answer:

nth term = t_{n} = 7.639(1.2)^{n - 1}

Step-by-step explanation:

Let us assume that the given sequence is a G.P.

Now, if the first term of the G.P. is a and the common ratio is r, then

Third term = t_{3} = ar^{2} = 11 .......... (1) and  

20th term = t_{20} = ar^{19} = 244.2 ........... (2)

Now, dividing equation (2) with equation (1) we get

\frac{ar^{19} }{ar^{2} } = \frac{244.2}{11} = 22.2

⇒ r^{17} = 22.2

⇒ r = 1.2.

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a(1.2)² = 11

⇒ a = 7.639 (Approx.)

Therefore, the general term of the sequence i.e. nth term = t_{n} = 7.639(1.2)^{n - 1} (Answer)

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