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
