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A cell phone company is selling their new phone. In the first week of them being on the market, 310 phones were sold. The company plans to increase sales by 17% each week. For example, they plan to sell 363 phones during week 2. The company will continue this for a year.


1. This is a geometric series. Give the first term (310), the common ratio (the actual value of the ratio, not just r), and an expression for the recursive rule. 


2. Write the explicit rule. Then answer how many phones will be sold during week 37. Round your answer to the nearest whole number of phones and show all work.


3. The company wants to know how many sales in all they can expect during the first year of selling the phones. Assume there are 52 weeks in a year. How many phones will be sold in all during the first year? Write and solve the expression for the correct partial sum of the series. Show all work, round your answer to the nearest whole number.

 Apr 14, 2018

Use Geometric Series formula:

S =F x ( 1 - R^N) / (1 - R), where S =Sum of the series, F = First term, R = Common ratio, N = Number of terms. The first term = 310, the common ratio =1.17. I don't know what you mean by "actual value of the ratio". 363 - 310 =53 extra phones, or 17%, were sold at the end of the 2nd week compared to the 1st week. But this number will go up by 17% every week. So, at the end of the 3rd week, you will have 53 x 1.17 =62 extra phones sold, and 62 x 1.17 =73 extra phones sold at the end of the 4th week....and so on. 


The 37th term will be =F x R^(N - 1), so sales for week 37 will be:

310 x 1.17^(37 -1) =310 x 1.17^36 =310 x 285 =88,350 - cell phones will be sold for week 37.


Use the above Geometric Formula to find total sales for the year:

S =310 x (1 - 1.17^52) / (1 - 1.17)

S =310 x (1 - 3,513) / (-0.17)

S =310 x  (-3,512) / (-.17)

S =310 x   20,659

S =6,404,290 - cell phone sold during the first year.

Note: Because of rounding off to whole numbers, the final total will be out by about 251. You may wish to check these calculations yourself and round off as you see appropriate.

 Apr 14, 2018

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