Write the first three terms of the pattern described. The starting number is 216. The rule is divide by three.
The number pattern described in this question follows a one-step rule. We know this because the rule only involves one operation. We’re only told to do one thing, and that’s to divide by three. So to find each new number in the pattern, we need to divide the previous number by three. And we need to do this twice because the question asks us to find the first three terms of the pattern. But what number do we begin with? Well, we’re told this is part of the question. We’re told that the starting number is 216. So let’s begin with 216 and start dividing by three. And if we look carefully at the number 216, we might see some digits that we can divide by three.
We know 21 is a number in the three times table and so is six. So we could partition 216 into 210 and six. Six divided by three equals two. Now, we know that 21 divided by three equals seven. So if we want to find the number of threes in 21 tens, the answer is going to be seven tens. And seven tens are the same as 70. 210 divided by three equals 70. Now, we can combine our two parts back together again to find the second number in our sequence. 70 plus two equals 72. So we can say 216 divided by three equals 72. Now, to find the third number in our sequence, we need to divide 72 by three.
Now, what multiples of three could be partition 72 into to help us? We know that 60 is a multiple of three. So what if we partition 72 into 60 and 12? 12 is also a multiple of three. Let’s divide both these parts by three. 12 divided by three equals four. Now, we know that six divided by three equals two. So six tens or 60 divided by three must be equal to two tens or 20. Now once again, we need to combine our two parts together to find the answer. 20 plus four equals 24. We followed a one-step rule to write a pattern involving three numbers. The rule was to divide every time by three. And our starting number was 216. So the first three terms of this pattern are 216, 72, and 24.