SOLUTION: Finish the following sequence: 5, 9, 21, 57, 165, ____, ____

Write the 5 numbers in a row

5     9      21      57     165

Between and underneath each adjacent pair of numbers,
write the difference between them, that is, the
right one minus the left one.  For instance, below
I began by subtracting 9-5 getting 4 and writing 4
below and between the 5 and the 9.  Next I subtracted
21-9 getting 12, and placed it below and between the
9 and the 21, and so on.

5     9      21      57     165
   4     12      36     108
 
Notice that that row is a gemetric sequence,

4x3=12, 12x3=36, and 36x3=108,

so the next two numbers in the second row should be

108x3=324 and 324x3=972

So let's write those two numbers on the second row,
in red:

5     9      21      57     165
   4     12      36     108      324      972  

Now we work backwards from the second row to the first
row.

Add the 324 to the 165, getting 489, and write it above
and between the 324 and 972 and beside the 165.

5     9      21      57     165       489
   4     12      36     108      324       972  

Fuinally, add the 972 to the 489, getting 1461, and write it above
beside the 489.

5     9      21      57     165       489      1461
   4     12      36     108      324       972 

So the next two numbers are 489 and 1461.

Edwin