A recursive formula for the sequence 2, 5, 26, 677 is f(t) = f(t-1)^2 + 1, where f(1) = 2.
Explanation
The provided sequence is: 2, 5, 26, 677,...
According to the provided reference, the next term in the sequence is calculated as (n-1)^2 + 1, where 'n' represents the previous term. Thus, the recursive function can be written as:
f(t) = f(t-1)^2 + 1
Example:
Let's verify the formula for the given sequence:
- f(1) = 2 (Given initial term)
- f(2) = f(1)^2 + 1 = 2^2 + 1 = 4 + 1 = 5
- f(3) = f(2)^2 + 1 = 5^2 + 1 = 25 + 1 = 26
- f(4) = f(3)^2 + 1 = 26^2 + 1 = 676 + 1 = 677
The formula accurately generates the provided sequence.
