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

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) (Show Source): You can put this solution on YOUR website!
.

Plot y = (sum of the AP, red)

and y = (sum of the GP, green)

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

Sa(n) = = in this case.

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

Sg(n) = .

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".

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