SOLUTION: In order to buy a new computer, you need $650. Your job offers in one of two ways: Option A: You earn $5 on the first day, $10 on the second day, $15 on the third day, and so on. E

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Question 1066655: In order to buy a new computer, you need $650. Your job offers in one of two ways: Option A: You earn $5 on the first day, $10 on the second day, $15 on the third day, and so on. Each day you are paid $5 more than the day before. Option B: You earn 2 cents on the first day, 4 cents on the second day, 8 cents on the third day, and so on. Each day you are paid double what you were paid the day before. Which option should you choose to earn $650 as quickly as possible, and how many days will it take to get there? Show all work.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Plot y = %285%2B%28%28x-1%29%2A5%29%2F2%29%2Ax (sum of the AP, red)

and y = 0.02%2A%282%5Ex-1%29 (sum of the GP, green)


For the first version, the total earning is the sum of the arithmetic progression

Sa(n) = %285%2B%28%28n-1%29%2A5%29%2F2%29%2An = 5n%2A%28n%2B1%29%2F2 in this case.


For the second version, the total earning is the sum of the geometric progression

Sg(n) = 0.02%2A%282%5En-1%29.


On arithmetic progressions, see the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
in this site.

On geometric progressions, see the lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
in this site.


Also, you have this free of charge online textbook in ALGEBRA-II
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topics "Arithmetic progressions" and "Geometric progressions".