<3,^4,>7,<6,^8,>14,<9,^12

Question

what is the next number in this sequence

 

Answer 1

First, look at the arrows. They have a clear pattern to them:

 

<, ^, >, <, ^, >, <, ^, ...

 

They go left, up, right, left, up, etc. Based on that pattern the next arrow should be >.

 

 

Now, look at the numbers. It's not clear what pattern they're following until you separate them by arrows:

 

<: 3, 6, 9, ...

^: 4, 8, 12, ...

>: 7, 14, ...

 

The left arrow pattern increases by 3, the up arrow pattern increases by 4, and the right arrow pattern increases by 7. So, since we want the next right arrow number, we want 14 + 7 = 21.

 

 

That means the next item in the pattern is:

 

>21