Problema Solution
the diagram below shows how tables and chairs are arranged in the school cafeteria. one table can seat 4 people, and tables can be pushed together. when 2 tables are pushed together, 6 people can sit around the table. create an explicit formula for a sequence that models this situation. use n=1 as the first term, representing how many students can sit at one table. how do the constants in your formula relate to the situation?
Answer provided by our tutors
Let f(n) is the function that models the situation.
We know that:
For n = 1
f(1) = 4
For n = 2
f(2) = f(1) + 2 = 4 + 1*2
For n = 3
f(3) = f(2) + 2 = 4 + 2*2
......
f(n - 1) = 4 + (n - 2)*2
f(n) = f(n - 1) + 2 = 4 + (n - 2)*2 + 2 = 4 + (n - 1)*2
f(n) = 4 + (n - 1)*2
4 is the students that can sit in 1 table.
2 is the number of additional students that can be sited each time a table is added.