What is the next number in the sequence? 3, 3, 6, 9, 15, 24, ...

Question

This is a question from my seventh grade summer packet. I need a little help on it. There are many questions but this is only one. I understand that it is about the number sequence, but I just can not find the pattern. Please help!

Answer 1

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.

 

 

Answer 2

3, 3, 6, 9, 15, 24,...

3+3=6

3+6=9

6+9=15

9+15=24

15+24=39

24+39=63

and so on