Patterns with Multiplication and Division

Another way to increase and decrease the terms in a sequence is to multiply and divide. Think about this sequence: 1, 6, 3, 18, 9, 54, 27…

Look at each term in the sequence. How did the terms change? How did 1 become 6? In this case, you know that the sequence uses multiplication and division, so you just need to figure out what to multiply 1 by to get 6. Of course, the answer is 6.

Now, look at the next two terms: 6 and 3. The numbers decreased, so you know the sequence used division. What do you divide 6 by to get 3? 6 ÷ 2 = 3. If you did not know that 6 ÷ 2 = 3, you would do 6 ÷ 3 to find what number it was divided by.

It appears that the rule is "multiply by 6, divide by 2," but you need to check the other terms to be sure.

When you check each term, you see that the rule "multiply by 6, divide by 2" works for the rest of the terms. What are the next two terms?

The next two terms are 162 and 81.