Question

41,29,17,5…..
The recursive function is _________ with A1=__

Answer 1

To identify the recursive function for the given sequence \(41, 29, 17, 5, \ldots\), let's first observe the differences between the consecutive terms:

- \(29 - 41 = -12\)
- \(17 - 29 = -12\)
- \(5 - 17 = -12\)

The differences are consistent: each term decreases by \(12\).

This suggests a recursive relationship where each term is derived from the previous term by subtracting \(12\).

We can define the recursive function as follows:

- Let \(A_n\) be the \(n\)-th term of the sequence.
- The recursive function can be defined as:
\[
A_n = A_{n-1} - 12
\]

- We also need to specify the initial term:
\[
A_1 = 41
\]

So the recursive function is \(A_n = A_{n-1} - 12\) with \(A_1 = 41\).