Question Video: Working with Number Patterns Involving Integers Mathematics

What are the missing numbers in this sequence: 576, 288, _, 72, 36, _, _?

02:17

Video Transcript

What are the missing numbers in this sequence: 576, 288, blank, 72, 36, blank, blank.

In order to find the missing numbers, we firstly need to find a pattern. As the numbers are decreasing as we move from left to right, the pattern will either be subtraction or division. We need to find how we can get from 576 to 288 and also from 72 to 36. We might immediately spot that 36 is a half of 72. This is because 72 divided by two is 36.

Let’s check to see if 288 is a half of 576. We will do this by dividing 576 by two. Five divided by two is equal to two remainder one. So we carry a one to the tens column. 17 divided by two is equal to eight remainder one. Finally, 16 divided by two is equal to eight. 576 divided by two is indeed 288.

We can therefore find the three missing numbers by continuing to divide by two when moving from left to right. The first missing number will be 288 divided by two. This is equal to 144. Our next missing number will be a half of 36 or 36 divided by two. This is equal to 18. 18 divided by two is equal to nine. So the last missing number is nine.

As the pattern of the sequence is dividing by two, the three missing numbers are 144, 18, and nine.

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