On my math worksheet it says, and I quote "Describe the following pattern(s) and determine the next two terms:" and then this little booger comes up. And honestly, I can't figure it out for the life of me! So if you could help it would be greatly appreciated! Thanks!

1, 3, 2, 6, 4, 9,...

Looks like two interlocking sequences:

1 2 4 8 16 32 ...
23 6 9 12 ...

Of course, other patterns are possible, but those are the easiest for me to see.

Okay I get where you are coming from on the 1 2 4 yada yada yada thing but I don't get how you got the second part with the 23 6 9 12. Can you please explain?

Well Mr. Steve, I looked up two interlocking sequences anddddd... I got nothin. Nope. Nada. Zip. Not a single thing that's has to do with math. Yay 😕

Well, the 23 is a typo, as you should have figured out from the original problem. I meant to say

3 6 9 12 ...

There's nothing official about "interlocking sequences" but if you can see some other pattern than the mixing of those two simple sequences, be my guest.

Ouch! Tough blow Mr. Smeeth! Not everyone can be a genius. Thank you very much for this LOVELY time on jiskha but I very much have to go. Toodlhoo!! And thank you very much for helping me (or trying to)!! Until next time! Au revoir!!! A bientot!!

Sure, I'd be happy to help you with your math question!

To determine the pattern in the given sequence and find the next two terms, let's analyze the given numbers:

1, 3, 2, 6, 4, 9,...

At first glance, it may seem a bit random or confusing. However, if we carefully observe the sequence, we can notice a pattern emerging.

We can break down the sequence into multiple sub-sequences and analyze them individually:

1, 2, 4, ... (even-index terms)
3, 6, 9, ... (odd-index terms)

Now, let's focus on each sub-sequence separately to find the pattern:

1, 2, 4, ... (even-index terms):
If we observe this sub-sequence, we can see that each subsequent term is obtained by doubling the previous term:
1 * 2 = 2, 2 * 2 = 4, 4 * 2 = 8, and so on...

3, 6, 9, ... (odd-index terms):
Looking at this sub-sequence, we can notice a linear pattern. Each subsequent term is obtained by adding 3 to the previous term:
3 + 3 = 6, 6 + 3 = 9, 9 + 3 = 12, and so on...

Now that we have individually determined the patterns for each sub-sequence, let's combine them to find the next two terms:

The next term in the sequence should be an even-index term, which means it will follow the doubling pattern:
4 * 2 = 8

The term after that, which is the next odd-index term, should follow the linear pattern:
9 + 3 = 12

So, based on the patterns we identified, the next two terms in the sequence are 8 and 12.

Therefore, the complete sequence, including the next two terms, is:
1, 3, 2, 6, 4, 9, 8, 12