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

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.

2) And what about the recursive rule for the original sequence, the approrpiate one is an = an-1 + n - 1, so the answer is lying in the second option from the scale.

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.

I am sure it's clear now!