Problems with patterns with rational numbers

In Looking for Patterns, we discovered that if a sequence of numbers increase or decrease by a regular amount, we can describe this as a number pattern. So far, we've only looked at numbers that increase or decrease by a whole number. Now we are going to build on that knowledge and find patterns with fractions and decimals as well.

Let's start by watching a video.

 

Summary

1. Decide whether the numbers are increasing or decreasing.
2. Work out how much they are increasing/ decreasing by each time.
3. Now you can write a rule to describe the pattern and to find the next number in the pattern (e.g. "Add $0.7$0.7 each time," or "Subtract $\frac{1}{3}$13​ each time.")
4. Use the rule you found to work out the next number in the pattern.

Worked Examples

Question 1

 

Question 2

 

Question 3