Complete the table below by following the pattern.
This table contains nine parts. But there are only six numbers in it. We can see that three parts of the table are empty. And these are the parts that we need to complete. The question instructs us to complete the table by following the pattern. But what pattern is it talking about? Where’s the pattern in this table? Well, there’re actually two patterns in the table that we could spot. And we could use either one to help us to complete it.
The first pattern we can spot is one that goes across the table from left to right. And the place to spot this pattern is in the first row because the first row is complete. The first number in the row is 700. And the second number is 730. The number has increased by 30. And if we look at the second two numbers in the row, we can see that this rule of adding 30 does work each time. 730 plus another 30 is 760.
Let’s use this first pattern that we’ve spotted to help us fill in the first missing number. The first number in the middle row is 710. Now, if we apply our plus 30 rule, we can find out what the missing number is. 30 is the same as three 10s. So let’s count on in 10s three times, starting with 710. 720, 730, 740. We followed the pattern of adding 30s. We move across the table to find our first missing number. 710 plus 30 equals 740.
Now, we could apply this pattern again to find the second two missing numbers. But we did say originally there were two patterns in this table. So let’s have a look at the other one and see if we can use this to find our final two missing numbers. As well as a pattern going across the table, there’s also a pattern going down the table. And perhaps, the best place to spot this pattern is in the center column because we’ve now got three numbers. It’s a complete column. The first number in the column is 730. And the next number is 740. And of course, to get from 730 to 740, we’ve added 10. Is this a rule for a pattern that we can see every time we go down the square? Yes, it is. To get from 740 to 750, we add 10 again. So we add 30 as we move across the table. But we add 10 as we move down the table.
Let’s follow this pattern to find our final two missing numbers. 10 more than 710 is 720. And 10 more than 770 is 780. We found these two missing numbers by adding 10 as we move down the table. But we could’ve found our final two missing numbers by applying the plus 30 rule. We could’ve added 30 to 750. And that way, we’d have found 780. And we would’ve needed to have worked backwards from 750 to find the remaining missing number. So we’d have subtracted 30. 750 take away 30 would’ve given us 720. So there are two patterns in the table. And we could’ve used either one to find the three missing numbers.
And if we read down the table from top to bottom and left to right, the three missing numbers are 740, 720, and 780.