Jon P. answered • 08/29/15

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Some sequences use one number to go to the next, such as adding a constant to a number in the sequence to get the next one. Let's see whether that's the case here:

3 to 3 -- difference of 0

3 to 6 -- difference of 3

6 to 9 -- difference of 3

9 to 15 -- difference of 6

15 to 24 -- difference of 9

Well, the steps from each number to the next are not the same, so that's out.

But do you see a pattern in the list of differences? 0, 3, 3, 6, 9

Notice that except for the first 0, the list of differences is the same as the first 4 numbers in the original sequence! That's the pattern.

How do you use that? The pattern tells us that each number is the previous number plus the one before it. Or a cleaner way to say it is, each number is the sum of the previous two numbers.

You have to start with the first two numbers:

3, 3 --> 6

3, 6 --> 9

6, 9 --> 15

9, 15 --> 24

Therefore the next number is 15 + 24 = 39.