SOLUTION: Which equation should I use for this problem? Summation? 1. You are running a foundation for a certain animal which is nearly extinct. Ms. Irene, a rich benefactor, offers two o

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Question 1117489: Which equation should I use for this problem? Summation?
1. You are running a foundation for a certain animal which is nearly extinct. Ms. Irene, a rich benefactor, offers two options for her donations:
Option 1: To give $1,000 on day 1, $999 on day 2, $998 on day 3, with the process to end after 1,000 days.
Option 2: To give $1 on day 1, $2 on day 2, $4 on day 3, for 19 days.
What formula should I use to know which one results in more money?
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
For option 1, you calculate the sum of 1000 terms of the arithmetic progression with the first term  1000  and the last term of  1.


The sum is  sum%5B1%5D = %28%281000%2B1%29%2F2%29%2A1000 = 500500 dollars.



For option 2, you calculate the sum of the first 19 terms of the geometric progression with the first term  1  and the common ratio of  2.


The sum is  sum%5B2%5D = %282%5E19-1%29%2F%282-1%29 = 2%5E19-1 = 524287 dollars.

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

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