[size=100][b]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.[/b][/size]

[size=200][b]Part 1[/b][/size]

[size=100][b]1)[/b] If there are [b]4[/b] seats in the first row, how many seats would there be in the [b]15[/b][sup]th[/sup] row?[/size]

[size=100][b]2)[/b] If there are [b]8[/b] seats in the first row, how many seats would there be in the [b]15[/b][sup]th[/sup] row?[/size]

[size=100][b]3) [/b]If there are [b]13[/b] seats in the first row, how many seats would there be in the [b]17[/b][sup]th[/sup] row?[/size]

[size=200][b]Part 2[/b][/size]

[size=100][b]4)[/b] 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.[/size]

[size=100][b]5) [/b]Write an explicit rule, [b]a[/b][sub]n[/sub], for determining the number of seats in the [b]n[/b][sup]th[/sup] row when the first row has 3 seats.[/size]

[b]6)[/b] Write an explicit rule, [b]a[/b][sub]n[/sub], for determining the number of seats in the [b]n[/b][sup]th[/sup] row when the first row has 11 seats.

[b]7)[/b] Write an explicit rule, [b]a[/b][sub]n[/sub], for determining the number of seats in the [b]n[/b][sup]th[/sup] row when the first row has 20 seats.

[size=100][b]8)[/b] Compare and contrast the rules written for [b]5)[/b], [b]6)[/b], & [b]7)[/b]. Explain why the similarities and differences occur the way they are.[/size]

[size=200][b]Part 3[/b][/size]

[size=100][b]9)[/b] Write a recursive rule, [b]a[/b][sub]n[/sub], for the number of seats in the [b]n[/b][sup]th[/sup] row when the first row has 6 seats.[/size]

[b]10) [/b]Write a recursive rule, [b]a[/b][sub]n[/sub], for the number of seats in the [b]n[/b][sup]th[/sup] row when the first row has 18 seats.

[b]11)[/b] Compare and contrast the rules written for [b]9)[/b] & [b]10)[/b]. Explain why the similarities and differences occur the way they are.