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: