Algebra Teachers: Use this trick when introducing geometric sequences.
This is an old problem
but it never ceases to fascinate students.
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!
Related Problems with Geometric Sequences: