Complete the pattern: 35000, 50000, 65000, what, what?
The first thing we can see about this pattern is that it’s an increasing pattern. In other words, the numbers that we can see get larger each time. We have 35000, 50000, 65000, and then two further numbers that we need to find. And the way to work out what they are is to look at the numbers we do know already and to see how they change. How do we get from 35000 to 50000? And is it the same as getting from 50000 to 65000? If it is, we’ve found a rule to the pattern. And we can use this rule to add to 65000 to find out what our first missing number is and then add to our first missing number to find our second missing number.
So let’s start from the beginning and see if we can spot a rule for our pattern. The first thing that we can notice about our pattern is that all three of the numbers that we’re given end in three zeros. They’re all a number of thousands. This means we can use number facts we already know to help us. For instance, what do we add to 35 to get a total of 50?
Well, if we add 10 to 35, we get 45. So we need to add another five on top of that to take us to 50. 35 plus 15 equals 50. Now we can apply this to our pattern. 35000 plus 15000 equals 50000. We’ve taken a number fact we already knew and applied it to counting in thousands.
Now not every pattern increases by the same amount every time. What happens if we add 15000 to 50000? Do we get 65000? And again, we can work with much smaller two-digit numbers. 50 plus 10 equals 60. And if we add the five, we get 65. 50000 plus 15000 does equal 65000. So we can say the rule for our pattern is to increase by 15000 each time.
Let’s apply our pattern twice more to find our two missing numbers. Firstly, what’s 15000 more than 65000? Well, we know 65 plus 10 equals 75. So if we add another five to that, we get 80. 65 plus 15 equals 80. And so 65000 plus 15000 equals 80000. Our first missing number is 80000.
Finally, what’s 15000 more than 80000? 80 plus 10 equals 90. And if we add the remaining five, we get 95. 80 plus 15 equals 95. And so 80000 plus 15000 equals 95000.
We looked at the first three numbers in our pattern and found that it was an increasing pattern. The rule for our pattern was to add 15000 each time. Once we worked out the rule, we could start with 65000 and make two jumps of 15000 to find our two missing numbers. Our completed pattern is 35000, 50000, 65000, and then our two missing numbers, 80000 and 95000.