Complete the pattern. Seven, 14, 28, something, something.
To work out the missing numbers, we need to find out what happens to each number to get to the next. And the first question we can ask ourselves is, is the pattern an increasing or decreasing sequence of numbers? Let’s draw a number line to find out. Now that we’ve put each of the numbers that we know on the number line, we can see that they’re getting larger each time.
What does this tell us? Well, it tells us that this is likely to be an addition or a multiplication pattern. Let’s have a look at each jump. Is the jump in between each of the numbers the same? Or does it change? We can write the jump from seven to 14 in two different ways. Seven plus seven equals 14. And seven times two equals 14. Both of these could be our pattern.
Let’s have a think about the next two numbers. To get from 14 to 28, we could add 14. Or we could multiply it by two. It’s important that we use the same rule every time. So our rule is multiply by two or double each number to get to the next. So to find the fourth number in the sequence, we need to multiply 28 by two.
What is 28 doubled? One method we can use to double two digit numbers is to partition them into tens and ones, to double those tens and ones, and then to combine them to find the answer. So we can start by partitioning 28 into 20 and eight. Now, let’s double each part. Double 20 is 40. And double eight is 16. Finally, let’s combine our double parts to find the answer. 40 plus 16 equals 56. And so 28 multiplied by two equals 56. And this is the fourth number in our pattern.
Let’s use the same partitioning method to double 56 and find the final number in our pattern. 56 can be partitioned into 50 and six. Let’s double each part. 50 doubled is 100. And six doubled is 12. Finally, we combine our double parts back together again. 100 plus 12 equals 112. And so we know that 56 multiplied by two is 112. And 112 is the last number in our pattern. And so our completed doubling pattern is seven, 14, 28, then 56, and 112.