Snapping Your Fingers

Algebra Teachers: Use this trick when introducing geometric sequences.

Snap your fingers.
Repeat in one minute.
Then snap your fingers again after 2 minutes (from the beginning).
Snap your fingers after 4 minutes (from the beginning).
Snap your fingers after 8 minutes (from the beginning).
Snap your fingers after 16 minutes (from the beginning).

How many snaps will I make in a year?

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:

Snap #	Time Elapsed
1	0 minutes
2	1 minute = 2⁰
3	2 minutes = 2¹
4	4 minutes = 2²
5	8 minutes = 2³
6	16 minutes = 2⁴
...	...
20	262,144 minutes = 2¹⁸
21	524,288 minutes = 2¹⁹
22	1,048,576 minutes = 2²⁰

So, the answer is 21 snaps in a year!!!!

There are 365 x 24 x 60 = 525,600 minutes in a year. The 21st snap would happen after 524,288 minutes. The 22nd snap would not occur until nearly a year later!

Related Problems with Geometric Sequences:

Salary Problem

Tearing Paper