Write the next three terms of the following sequence, minus two, minus one, zero.
At the moment, our sequence only contains three numbers, or three terms, minus two, minus one, and zero. The question asks us to write the next three terms, or the next three numbers. So, we get to zero, but what happens next?
Well, the answer is hidden in the numbers that we know already. We need to look carefully at those numbers and ask ourselves, how do we get from one number to the next number? What’s the rule behind the sequence? And once we know the rule, we can then carry on using the rule to find the next three numbers.
The first thing to notice about the numbers that we know already is this negative sign here. If we look carefully, we can see another negative sign in front of the one. It might be easy not to notice these negative signs, in which case we’d make a mistake with our answer. These numbers are less than zero. They’re negative numbers. But are they increasing or decreasing?
Again, it’s easy to make a mistake here and to look at the digits and to think two, one, zero, the numbers are going down by one each time. But let’s look at a number line to see how the numbers really are behaving. Minus two is two below zero. To get from minus two to minus one on the number line, we move one number to the right. We add one. Minus two add one equals minus one. So, even though the digit itself goes down, what we’re doing is increasing the number by one.
Then to get from minus one to zero, we have another jump of one number. Minus one and one takes us to zero. So, the rule for our sequence seems to be adding one each time, we’re just counting upwards. And so, the next three numbers in the sequence are easy to spot, one, two, and three. And so, the rule for our sequence was to add one, or just to count on each time, minus two, minus one, zero, and now the next three terms that we needed to find, one, two, and three.