The numbers in this sequence increase by 14 each time. And then the sequence shows a missing number, 82, 96, another missing number, 124, 138, and then a third missing number. Write the missing numbers.
In this question, we’ve been given a sequence of seven numbers. But three of the numbers are missing. So we need to apply the rule to find out what they are. What is the rule in this sequence? Well, often a question will ask us to work out what the rule is. But in this problem, we’re given the rule as part of the question. The numbers in the sequence increase by 14. So as we move from each number to the next in the sequence, we add 14 each time.
If we look at our three missing numbers, one of them is a little bit more tricky to work out than the others. Which is it? Well, it’s the first missing number in the sequence. Because it’s the first number, we don’t have a number to add 14 to, to give us the missing number. With the other two missing numbers, we do have the number that comes before in the sequence. So how are we going to work out our first missing number?
Let’s use the number 82 to help. At the moment, we know that our missing number plus 14 equals 82. And so we can start with 82 and take away 14 to give us our missing number. Let’s change the arrow on our sequence to show how to calculate the first missing number. Start with 82, take away 14 to give us our missing number. 82 take away 10 is 72 and then take away four gives us 68. Let’s just check that works. 68 plus 10 equals 78, and then plus four equals 82. So there is a difference of 14.
The next missing number in the sequence is a little bit easier because we know the number that comes before. What is 96 plus 14? Let’s add 10 and four, as before. 96 plus 10 equals 106. And we know that six and four make the nearest 10. So 106 plus four equals 110. Again, we can quickly check that the number is correct by adding 14 to 110. And we can see that it does equal the next number in the sequence which is 124.
Finally, let’s work out the last missing number. Again, we know the number before it. So we just need to add 14 to 138. 138 plus 10 equals 148, and then plus the four equals 152. How did we find our three missing numbers? Well, we didn’t have to work out the rule. We were told it in the question. We knew that the numbers increased by 14 each time. We knew that this meant there was a difference of 14 between each number.
For two of the missing numbers in our sequence, we knew the number that came before. And so we just added 14 to the number that came before to find the answer. One of our numbers came right at the start. And so we didn’t have a number to add 14 to. So we used our knowledge that there’s a difference of 14. We started with 82 and we subtracted 14 to find the number that came before. And so the missing numbers are 68, 110, and 152.