Video: Recognising Number Patterns

Complete the sequence: 5939, 5932, 5925, _, _, _, _.

03:57

Video Transcript

Complete the sequence: 5939, 5932, 5925, what, what, what, and what?

All the whats as we read the question show that there are four missing numbers to this sequence. And the question is asking us to find them to complete the sequence. To do this, we need to look at the three numbers that we’ve been given already and try and work out what the rule for the sequence is. Our numbers are 5939, 5932, and 5925. What do we notice about these numbers?

Well, the first thing we can say about the sequence is that it’s a decreasing pattern. As we go from one number to the other, the numbers are getting less and less. But by how much? Our first number has five thousands, nine hundreds, three tens, and nine ones. Our second number has five thousands, nine hundreds, three tens, and two ones. The number of thousands has stayed the same, as has the number of hundreds and also the number of tens.

In fact, the only part of the number that’s changed is the ones. We’ve gone from nine ones to two ones. How do we get from nine to two? Well, we know that two and seven make nine. So nine take away seven will leave us with two. Let’s see whether subtracting seven is the rule for the pattern. We’ll have a look at the next number.

We have five thousands, nine hundreds. This time, the tens digit has changed and the ones digit. If we look at the number we were starting from, it ended in 32. And 32 take away seven does equal 25. The next number in the sequence will be 5925.

Now that we know what the rule for the sequence is, we can find our remaining four numbers. We know that 25 take away seven equals 18. And so 5925 take away seven will be 5918. 5918 has eight ones. So we can subtract seven quickly. Eight take away seven equals one. So the next number in our sequence is 5911. Seven plus four equals 11. So if we take away seven from 5911, we’re left with 5904.

Finally, we can split the seven that we want to subtract into four and three. If we take away four from 5904, we’re left with 5900. Now if we take away the remaining three, we’re left with 5897.

We’ve found that our sequence was a decreasing one and that the rule was to take away seven each time. The completed sequence is 5939, 5932, 5925, and then our four missing numbers, 5918, 5911, 5904, and 5897.

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