Michelle B.

Sequences & Series

Problem:

A cell phone company plans to market a new smartphone. They have already sold 510 units during the first week of the campaign. They plan to increase sales by 12% each week. For example, they plan to sell about 571 units during week 2. They want to continue this for a year (52 weeks).

A. Is this an Arithmetic or Geometric Series? I hope you agree this is a Geometric series. Write the values of the first term, the common ratio, and an expression for the recursive rule. Use the actual value of the common ratio in the recursive rule, not just “r”.

B. Write the explicit rule so that you can find any term in the series without finding the previous terms first. How many phones will be sold during week number 37? Show all your work. Round your answer to the nearest whole number of cell phones.

C. The payroll department wants to know how many sales they can expect during the first year of the campaign. Assume there are 52 weeks in a year. How many phone will be sold total during the entire first year? Write and evaluate the expression for the correct partial sum of the series. Show all your work. Round your answer to the nearest whole number.