# Mr. Polya's Theater Hall

- Author:
- Mark Beckwith

- Topic:
- Arithmetic

**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

**15**

^{th}row?

**2)**If there are

**8**seats in the first row, how many seats would there be in the

**15**

^{th}row?

**3)**If there are

**13**seats in the first row, how many seats would there be in the

**17**

^{th}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,

**a**

_{n}, for determining the number of seats in the

**n**

^{th}row when the first row has 3 seats.

**6)**Write an explicit rule,

**a**

_{n}, for determining the number of seats in the

**n**

^{th}row when the first row has 11 seats.

**7)**Write an explicit rule,

**a**

_{n}, for determining the number of seats in the

**n**

^{th}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,

**a**

_{n}, for the number of seats in the

**n**

^{th}row when the first row has 6 seats.

**10)**Write a recursive rule,

**a**

_{n}, for the number of seats in the

**n**

^{th}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.