Page 240 - Mind Games The Aging Brain and How to Keep it Healthy

224 • Chapter 7

it. For a more in-depth treatment of the sequence, visit the
Web site www.mathacademy.com/platonic_realms/en-
cyclop/articles/fibonac.html.
This next sequence takes you up a notch on the difficulty
scale! Find the next term in this sequence:
1,101,1101,101101, . . .
Follow these steps:
1. Identify the question. You need to find the next num-
ber in the sequence.
2. Note all of the facts you already have. You have four
terms already. They appear to be a collection of 1s and 0s.
3. Determine what is missing. You don’t know the pattern.

4. Do some creative work. Take a look at how each term is
built from the terms before it.

Notice from 1 to 101, it looks as if 1, 101,
you put a 10 in front of the 1 to
make the second term.

But you didn’t do that for the third 1, 101, 1101,
term.You put a 1 in front of the
second term.
Notice the fourth term. Here you are 1, 101, 1101, 101101
back to putting a 10 in front.

So, now you guess that you put a 1 1, 101, 1101, 101101, 1101101
in front of the fourth term to
make the fifth term.
Notice that the word is guess. That’s the best you can do
for inductive reasoning. Whatever pattern you make up,
someone else might devise a different pattern.
Here are a few other common strategies for finding the
next number in a sequence. Consider the sequence 1, 3, 5, 7, 9,
11, 13, . . . What is the next number in the sequence? You
might recognize the sequence as a list of the odd numbers.
Then next number would be 15. If you didn’t recognize the
odd numbers, you might try looking for a pattern. You
would see that the numbers go up by 2 each time. So the
next number would be 13 + 2 = 15.