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

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(52780) (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   =  = 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   =  =  = 524287 dollars.

----------------
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.

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