4 37 180 793 2566 6659 14842 29635 33 143 613 1773 4093 8183 14793 110 470 1160 2320 4090 6610 360 690 1160 1770 2520 330 470 610 750 140 140 140
See above. Forget about the colored values for the moment. Your first step is to write out the given sequence with spaces between each number. Then, in the next line, between each of the numbers in the line above, write the difference between the number above and to the right and the number above and to the left. For example, your first entry on the second line is 33 because that is the difference 37 minus 4. Continue the process until you have filled in all of the values in the second row. Examine the values in the second row. If they are not all the same, continue the process to create a third row. Keep going until you have a row where all of the values are the same -- like the fifth row in this example.
Next, add an additional entry to the last row. In this example, the red 140. Then add this new entry to the number above and to the left. Place the sum in the next open spot in the row above -- the red 750. Continue the process until you have entered a new term to the first row. In this example, the green 29635.
By the way, if you attempt this process and you end up with only one value left in your bottom row, you either have insufficient terms in your original series or perhaps you have made an arithmetic error.
John
My calculator said it, I believe it, that settles it
