Salary Problem

Algebra Teachers: Use this trick when introducing geometric sequences.
This is an old problem but it never ceases to fascinate students.

You are offered the following proposition:
You are to work for 30 days.
On the first day, you will be paid a penny.
On the second day, you will be paid 2 cents.
On the third day, you will be paid 4 cents.
On the fifth day, you will be paid 8 cents.
How much would you make for the thirty days?
Do not let your students use calculators!
Just have them give you a guess at first.

Now have them construct a table and look for a pattern:
Day # Amount Earned on that Day Total Earned
1 .01 .01
2 .02 .03
3 .04 .07
4 .08 .15
5 .16 .31
6 .32 .63
7 .64 $1.27
8 $1.28 $2.55
... ... ...
30 229 / 100 = $5,368,709.12 $10,737,418.23

So, you earn over ten million dollars in the thirty days, making $5,368,709 on the last day!

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Related Problems with Geometric Sequences:

      Tearing Paper

      Snapping Your Fingers

      Homework Problem

Math Tricks

Mr. P's Puzzles and Games Page