# Mr. Polya's Theater Hall

﻿Mr. Polya would like to give back to his community by building a Theater Hall to host community events. The design for the hall allows for at most 25 rows of seats that can be arranged as in the diagram below.
﻿Part 1
﻿1) If there are 4 seats in the first row, how many seats would there be in the 15th row?
﻿2) If there are 8 seats in the first row, how many seats would there be in the 15th row?
﻿3) If there are 13 seats in the first row, how many seats would there be in the 17th row?
﻿Part 2
﻿4) What is the relationship between the number of seats in consecutive rows? Does this relationship change when the number of seats in the first row changes? Explain.
﻿5) Write an explicit rule, an, for determining the number of seats in the nth row when the first row has 3 seats.
6) Write an explicit rule, an, for determining the number of seats in the nth row when the first row has 11 seats.
7) Write an explicit rule, an, for determining the number of seats in the nth row when the first row has 20 seats.
﻿8) Compare and contrast the rules written for 5), 6), & 7). Explain why the similarities and differences occur the way they are.
﻿Part 3
﻿9) Write a recursive rule, an, for the number of seats in the nth row when the first row has 6 seats.
10) Write a recursive rule, an, for the number of seats in the nth row when the first row has 18 seats.
11) Compare and contrast the rules written for 9) & 10). Explain why the similarities and differences occur the way they are.