# Lesson 1

A Towering Sequence

- Let’s explore the Tower of Hanoi.

### Problem 1

Here is a rule to make a list of numbers: Each number is the sum of the previous two numbers. Start with the numbers 0 and 1, then follow the rule to build a sequence of 10 numbers.

### Problem 2

A sequence starts \(\frac{1} {2}, \frac{1}{4}, \frac{1}{8}, \dots\)

- Give a rule that the sequence could follow.
- Follow your rule to write the next 3 terms in the sequence.

### Problem 3

A sequence of numbers follows the rule: multiply the previous number by -2 and add 3. The fourth term in the sequence is -7.

- Give the next 3 terms in the sequence.
- Give the 3 terms that came before -7 in the sequence.

### Problem 4

A sequence starts 0, 5, . . .

- Give a rule the sequence could follow and the next 3 terms for that rule.
- Give a
*different*rule the sequence could follow and the next 3 terms for that rule.