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!

Related Problems with Geometric Sequences:

Tearing Paper

Snapping Your Fingers