Question

In Exploration you explored the differences involving sequences in the form f(n) = an^k. Which of the following is the strongest conjecture for a sequence with the kth power?

Option 1: The constant difference occurs when a = k.
Option 2: The constant difference occurs on the kth round and the difference is a - k!.
Option 3: The constant difference would be 5.
Option 4: The constant difference occurs on the kth round and the difference is k.

Answer 1

The strongest conjecture for a sequence with the kth power is when the constant difference occurs when a = k.

Step-by-step explanation:

The strongest conjecture for a sequence with the kth power is Option 1: The constant difference occurs when a = k.

This means that if a sequence is in the form f(n) = an^k, the constant difference occurs when the value of 'a' is equal to the value of 'k'.

For example, if the sequence is f(n) = 2n^2, the constant difference occurs when 'a' (which is 2 in this case) is equal to 'k' (which is also 2 in this case).