Adding a series of quadruples

1. Have a friend choose a single digit number. (No restrictions for experts.)
2. Ask your friend to jot down a series of quadruples (where the next term is always four times the preceding one), and tell you only the last term.
3. Ask your friend to add up all these terms.
4. You will give the answer before he or she can finish: The sum of all the terms of this series will be four times the last term minus the first term, divided by 3.

   Example:

1. If the number selected is 5:
2. The series jotted down is: 5, 20, 80, 320, 1280.
3. Four times the last term (1280) minus the first (5):
   4000 + 800 + 320 - 5 = 5120 - 5 = 5115
   Divide by 3: 5115/3 = 1705
4. So the sum of the quadruples from 5 through 1280 is 1705.

   See the pattern? Here's one for the experts:

1. The number selected is 32:
2. The series jotted down is: 32, 128, 512, 2048.
3. Four times the last term (2048) minus the first (32):
   8000 + 160 + 32 - 32 = 8,160
   Divide by 3: 8160/3 = 2720.
4. So the sum of the quadruples from 32 through 2048 is 2720.

Practice multiplying from left to right and dividing by 3. With practice you will be an expert quad adder.