Question 261707
Finish the following sequence: 5, 9, 21, 57, 165, ____, ____
<pre><font size = 4 color = "indigo"><b>
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      <font color = "red">324      972</font>  

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       <font color = "red">489</font>
   4     12      36     108      <font color = "red">324       972</font>  

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

5     9      21      57     165       <font color = "red">489      1461</font>
   4     12      36     108      <font color = "red">324       972</font> 

So the next two numbers are 489 and 1461.

Edwin</pre>