i.
To identify: A rule for the number of games played in the nth round. For what values of n does your rule make sense?
A regional soccer tournament has 61 participating teams. In the first round of the tournament. 32 games are played. In each successive round, the number of games played decreases by a factor of one half.
The required rule is
Given information:
The given terms are
Explanation:
Consider the given sequence.
It is given that
The general formula for a geometric sequence is
In the first round the number of games played is
In the second round the number of games played decrease by one half thus this is
In the third round the number of games played decrease by one more half thus this is
Based on this procedure, there are
This rule have sense until we come to final game, so that is when the number or played games comes to 1
Let determine
Therefore, this rule make sense only if there are
ii.
To calculate: The total number of games played in the regional soccer tournament.
The total number games played
Given information:
The given terms from above calculation
Explanation:
Consider the given sequence.
It is given that
The general sum formula for a geometric sequence is
Put the value of
Therefore, the total number of games played in the regional soccer tournament is
Chapter 7 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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