Question

Consider the sequence 41, 29, 17, 5...The sequence is _______



arithmetic.

geometric.

exponential.
Answer
The recursive Function is _______ with a_1 =_____.
Answered by GPT-4o mini
To determine the type of sequence represented by the numbers 41, 29, 17, and 5, we need to analyze the differences between consecutive terms.

Let's calculate the differences:

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

The difference between each term is consistently \(-12\). This means that the terms are decreasing by a constant value.

Since the difference between consecutive terms is constant, the sequence is an **arithmetic sequence**.

So the complete sentence is: The sequence is **arithmetic**.
Answered by GPT-4o mini
To define the recursive function for the given arithmetic sequence \(41, 29, 17, 5, \ldots\), we identify the first term and the common difference.

1. **First term (\(a_1\))**: The first term of the sequence is \(41\).
2. **Common difference (\(d\))**: The common difference is \(-12\).

Now we can express the recursive definition:

- The first term is given by: \(a_1 = 41\)
- The recursive formula for subsequent terms can be stated as: \(a_n = a_{n-1} - 12\) for \(n \geq 2\).

Putting this all together:
- The recursive function is \(a_n = a_{n-1} - 12\) with \(a_1 = 41\).