Find the common difference:
3 6 17 42 87 158
\ / \ / \ / \ / \ /
3 11 25 45 71
\ / \ / \ / \ /
8 14 20 26
\ / \ / \ /
6 6 6
The actual difference numbers don't matter. The important thing is that the differences are the same in the third row of differences. Hence, the sequence can be modeled with a 3rd-degree polynomial.
The value of the function at
Hence
Or, more simply put
Then, when
In a like manner we can derive:
And
Solve the 4X4 system of linear equations to find the coefficients of the 3rd-degree polynomial that models your desired sequence.
John
My calculator said it, I believe it, that settles it