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!

Links:

Related Problems with Geometric Sequences:

      Salary Problem

      Tearing Paper

      Homework Problem

Math Tricks

Mr. P's Puzzles and Games Page