7,-20,61

The first differences are -20-7 and 61-(-20) or -27 and 81

The second difference is 81-(-27) or 108

Make the table with the terms in the first column, the first
differences in the second column and the third difference in
the third column:

  7   -27   108
-20    81
 61

To get three more terms, extend the table by putting three more 
second differences of 108's in the last column:

  7   -27   108
-20    81   108
 61         108
            108

Now work backward by adding.  That is:

Add the second 108 to the 81 just left of it, getting 189, 
and put that under the 81:

  7   -27   108
-20    81   108
 61   189   108
            108

Add the 189 to the 61 just left of it, getting 250, 
and put that under the 61:

  7   -27   108
-20    81   108
 61   189   108
250         108
 
Add the next 108 to the 189 just left of it, getting 297, 
and put that under the 189:

  7   -27   108
-20    81   108
 61   189   108
250   297   108

Add the 297 to the 250 just left of it, getting 547, 
and put that under the 250:

  7   -27   108
-20    81   108
 61   189   108
250   297   108
547


So the sequence is now 7,-20,61,250,547, to 5 terms.

To get the 6th term do the same thing with the 108 at the bottom
of the third column.  I won't tell you the 6th term, just to be mean. :)

Edwin