Numerical patterns with a constant multiplier: Explanation

2, 4, 8, 16. These numbers are all connected somehow. How, exactly? Let’s see. How do we get from 2 to 4?

We could add 2. Will that work to get from 4 to 8? Hmm, 4 add 2 is 6, not 8. Let’s try a different way. How else could we get from 2 to 4?

We could double 2. Two doubled is 4. And what happens if we double 4? 4 doubled is 8. Perfect!

How about if we double 8? 8 doubled is 16. We can say that these numbers form a pattern, and the pattern’s rule is: starts at 2 and doubles. Let’s look at another pattern. 20, 10, 5, 2.5.

This pattern is different: it starts big and gets smaller. So we know that neither adding nor doubling will help us. Let’s try subtracting. To get from 20 to 10, we could subtract 10. If we subtract 10 again, we get…0.

Hmm, subtracting doesn’t work for this pattern. How else could we get from 20 to 10? We could halve 20. That gives us 10. How about if we halve 10?

That would be… 5! And half of 5 is… 2.5! The rule for this pattern is: starts at 20 and halves. Take a look at the next pattern and see if you can find the rule. This pattern starts at 3 and doubles.

Now we know the pattern’s rule, let’s see if we can carry it on. What comes after 24? Let’s double it. 24 add 24 is… 48! We’ve used the pattern’s rule to help us carry on the pattern.

Knowing a pattern’s rule can help us with something else, too. This pattern is missing a number. 36, 18, something, 4.5. First, let’s find the rule. To get from 36 to 18 we… halve.

Now let’s halve 18, to see if that works for the missing number. Half of 18 is… 9. And half of 9 – is that 4.5? It is! We got the missing number right.

Take a look at this last pattern. See if you can find the pattern’s rule, find the missing number, then carry it on. Good luck! This pattern’s rule is: starts at 208 and halves, and the missing numbers are 26 and 6.5. We’ve learned to find the rule for patterns that get bigger or smaller by doubling or halving.

And we know that we can use a pattern’s rule to carry on the pattern or find a missing number.