3 -6 12 4 20

List them in a column

 3
-6
12
 4
20

Subtract each number from the one just below it 
and write the difference out besides it.

 3 -9 
-6 18
12 -8
 4 16
20

The second column goes -9,18,-8,16
That has this pattern: -9,18,-8,16,-7,14,-6,12,-5,10,-4,8,...
So put -7 below 16 and add 20, get 13.

 3 -9   
-6 18 
12 -8
 4 16
20 -7
13
---------------------------

Next number in this pattern 

Do the same as the preceding sequence:

 7   9 
16  -8
 8  19
27 -18
 9

That has this pattern:  9,-8,19,-18,29,-28,39,-38,48,-47,...

The second column goes 9,-8,19,-18
That has this pattern: 9,-8,19,-18,29,-28,39,-38,48,-47,...
So put 29 below -18 and add 9, get 38.

 7   9 
16  -8
 8  19
27 -18
 9  29
38

--------------
Try that method with the next one:

  2   5  
  7  21
 26  75
101 299
400

That doesn't seem to work here.  Let's try dividing
instead of subtracting

  2  3.5  
  7  3.7142...
 26  3.8846...
101  3.96049...
400

Those all round up to 4, and they're getting closer 
and closer to being like a geometric sequence with
common ratio 4, so let's see what happens when we 
multiply them all by 4.

  2   8  
  7  28
 26 104 
101 404
400

From   8 we must subtract 1 to get 7,
From  28 we must subtract 2 to get 26,
From 104 we must subtract 3 to get 101,
From 404 we must subtract 4 to get 400,

  2   8-1  
  7  28-2
 26 104-3 
101 404-4
400    

So to get the next number, we multiply 400 by 4 and subtract 5,

   2    8-1  
   7   28-2
  26  104-3 
 101  404-4
 400 1600-5
1595

-------------------------------------

7 21 8 72 9

We see a pattern with 1st, 3rd, and 5th
terms, 7, 8, and 9, and we notice that 21 
is 7x3, and that 72 is 8x9. And 9 is 32. 
So the 5th term 9 must be multiplied by 
the next power of 3, which is 33 or 27.
So the next term is 9x33 or 9x27 or 243.

Edwin