Final answer:
A difference table is not effective for Fibonacci numbers because they are defined recursively and do not form a polynomial sequence. The differences will not simplify to a constant or reveal a simple expression as they would for polynomial sequences.
Step-by-step explanation:
When using a difference table to determine Fibonacci numbers, the process will not be as straightforward as it is for sequences with polynomial behavior. The Fibonacci sequence is defined recursively, with each term being the sum of the two preceding ones, starting from 0 and 1. A difference table is more useful for sequences where the n-th term can be expressed as a polynomial of n. Here's why a difference table is not effective for Fibonacci numbers:
The first difference of Fibonacci numbers does not settle into a constant, which it would for a linear function.
The second difference of the Fibonacci numbers will also not be constant; this continues for higher-order differences.
The difference table will keep growing with increasing complexity and will not show a pattern of zeros that indicates a polynomial relationship.
In conclusion, a difference table will not magically reveal a simple expression for Fibonacci numbers, because they do not form a polynomial sequence. They are defined by a recursive formula, and each number in the sequence depends on its predecessors in a non-polynomial manner.