Find the next three terms in the following sequence: 73000, 72000, 70000, what, what, what.
We’re given a sequence of three numbers and asked to find the next three terms in the sequence. These are the three blanks on the end. With this question, it might be very easy to make a mistake just by reading the question quickly and thinking that we know the answer. We might see the first number 73000, look at the second number which is 72000, and think to ourselves that we’ve spotted the pattern already. It’s a decreasing pattern. So the rule for the pattern must be take away 1000 every time. And so we can jump from 70000 to 69000, then 68000, and finally 67000.
But we can’t just answer this quickly. We need to give it a little bit more thought. We can’t base a sequence on a difference between two numbers. We need to look at more numbers. So let’s look at the next two numbers in the sequence. What happens to the number 72000 to get to 70000. We don’t take away 1000. We take away 2000. 72000 take away 2000 leaves us with 70000. So by looking at more of the numbers, we’ve got a better idea of what the rule might actually be. First, we take away 1000. Then we take away 2000.
So how do we think the sequence is going to continue now? We need to subtract 3000, then 4000, and then 5000. The number that we’re subtracting is increasing by 1000 each time. We know that 70 take away three equals 67. So 70000 take away 3000 equals 67000. Our first missing number is 67000. 67 take away four equals 63. So 67000 take away 4000 equals 63000. Our second missing number is 63000 then. We can find our final number by taking away 5000. And again, we can use our known facts to help. 63 take away five leaves us with 58. And so we can complete the subtraction using thousands to give the answer 58000.
Instead of just looking at the first two numbers and thinking that we knew the pattern straight away, we looked at the first three numbers. And we noticed that the number that we were subtracting each time was getting larger. This helped us to spot the pattern in the sequence. And that was to take away one more lot of 1000 each time. In other words, the total that we were taking away was increasing by 1000. So we found our missing numbers by taking away 3000, then 4000, and then 5000. The missing numbers in the sequence are 67000, 63000, and 58000.