SOLUTION: Find x in the following sequence: 180,60,24,128,x,16

Here is one way to get it.

Make a difference table by listing the sequence in the first
column.  Then subtract every number from the number directly
below it and write it out to the right of that number until
you can get a column with the same number everywhere in it.


180   -120      84       56    x-428
 60    -36     140    x-372   748-4x
 24    104   x-232   376-3x
128  x-128  144-2x  
  x   16-x  
 16

To make the last column have the same number we set the
two expressions equal:

Set    x-428 = 748-4x

solve that and get get x = 1176/5 = 235.2

Answer x = 235.2

Sequences can have more than one solution.  This is just one
of many.  Your teacher will likely have another one in mind, but
this one is just as good as the one he or she has in mind.  There
are lots of others too.  Don't let your teacher convince you that
there is only one solution, because there are many.  This is only
one.

Edwin