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!