I'm having trouble on this problem.

Question

Write both an explicit and recursive rule for the geometric sequence that models the situation. Use the sequence to answer the question asked about the situation. 

 

The Alphaville Youth Basketball committee is planning a single-elimination tournament. the committe wants the winner to play 4 games. How many teams should the committee invite?

Answer 1

Okay, however many teams you start with, after one round, you are left with half.  Half winners, half losers.  Recursive gives you the new number using the previous term.  Explicit allows you to get any term you want from the first term.

 

Recursive: A_n+1=(1/2)A_n ~ half of the current term

Explicit: A_n=A₁(1/2)^n-1 ~ basic format for geometric series

 

Solution:

1=A₁(1/2)^4-1 ~ You want one winner, so the term is 1 after the desired 4 games

1=A₁(1/2)³

1=A₁/8

A₁=8 You want 8 teams to come