Sequences and Series

1. Denise is designing the seating arrangement for a concert an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the first row can only have 11 seats. Help Denise plan the rest of the seating by solving for how many seats are in row 18. Then explain to Denise how to create an equation to predict the number of seats in any row. Show your work, and use complete sentences.

2. Arthur has decided to start saving for a new computer. His money is currently in a piggy bank at home, modeled by the function s(x) = 85. He was told that he could do the laundry for the house and his allowance would be a(x) = 10(x – 1), where x is measured in weeks. Explain to Arthur how he can create a function that combines the two, and describe any simplification that can be done.

3. Brian has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.17 times as many villagers. The game gave Brian 8 villagers to start with. Help Brian expand his empire by solving for how many villagers he can create with 16 towns. Then explain to Brian how to create an equation to predict the number of villagers for any number of towns. Show your work and use complete sentences.

4. Christina has some money at home, and the amount is modeled by the function h(x) = 103. She read about a bank that has savings accounts that accrue interest according to the function s(x) = (1.03)x – 1. Using complete sentences, explain to Christina how she can combine her functions to create a new function, and explain what this new function means.

5. Phillip received 75 points on a project for school. He can make changes and receive two-tenths of the missing points back. He can do this 10 times. Create the formula for the sum of this geometric series, and explain your steps in solving for the maximum grade Phillip can receive.