Difference table method:
1. List them in the first column.
2. Subtract each number from the one just below it and write it
in a column out to the right.
3. Continue making columns until there are just two numbers
in the rightmost column.
3. Assume that the rightmost column contain an arithmetic sequence
beginning with those two numbers, having a common difference of their difference.
91 -34 3
57 -31 48
26 17
43
Those two numbers 3 and 48 differ by 48-3=45, so we extend the sequence
of the last column by using a common difference of 45:
3, 48, 93, 138, 183, 228.
We just want one more term, so put 48+45=93 in the last column under the 48:
91 -34 3
57 -31 48
26 17 93
43
Now work backward from right to left, add 93+17=110 and place it
under the 17.
91 -34 3
57 -31 48
26 17 93
43 110
Now add 110+43=153 and place it under the 43
91 -34 3
57 -31 48
26 17 93
43 110
153
That's the next term.
So the sequence is now 91, 57, 26, 43, 153
If you wanted to get the next term, you'd put
the next term of the arithmetic sequence
3, 48, 93, 138, 183, 228, under the 93, which
is 138, and work backwards the same way.
The sequence goes
91, 57, 26, 43, 153, 401, 832, 1491, 2423, ...
You can continue ANY sequence this way, but
there are many other ways, that will give
different answers.
Edwin
