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The problem you're working on presents a recursive sequence defined as follows:

\[
f(1) = 10, \quad f(n) = f(n-1) - 1.5 \text{ for } n \geq 2.
\]

Let's break this down:

### Part (a) 
**Is this sequence arithmetic, geometric, or neither?**

An arithmetic sequence has a constant difference between consecutive terms. The recursive formula \(f(n) = f(n-1) - 1.5\) subtracts 1.5 from the previous term each time, which indicates a constant difference of \(-1.5\). Therefore, this is an **arithmetic sequence**.

### Part (b)
**List at least the first five terms of the sequence.**

Using the recursive relation:
- \(f(1) = 10\)
- \(f(2) = f(1) - 1.5 = 10 - 1.5 = 8.5\)
- \(f(3) = f(2) - 1.5 = 8.5 - 1.5 = 7\)
- \(f(4) = f(3) - 1.5 = 7 - 1.5 = 5.5\)
- \(f(5) = f(4) - 1.5 = 5.5 - 1.5 = 4\)

So, the first five terms of the sequence are:
\[
10, 8.5, 7, 5.5, 4.
\]

Let me know if you need further details or explanations!

Here are 5 related questions:
1. How can we generalize the formula for any arithmetic sequence?
2. What would the 10th term of this sequence be?
3. How can we find the sum of the first \(n\) terms of an arithmetic sequence?
4. Can a recursive formula be used to represent geometric sequences as well?
5. What are the applications of arithmetic sequences in real-world problems?

**Tip:** For arithmetic sequences, you can always use the formula \( a_n = a_1 + (n-1)d \), where \(d\) is the common difference.

Here is the recursive definition of a sequence: f(1) = 10, f(n) = f(n-1) - 1.5 for n ≥ 2. a. Is this sequence arithmetic, geometric, or neither? b. List at least the first five terms of the sequence.

Explore the recursive sequence where f(1) = 10 and f(n) = f(n-1) - 1.5 for n ≥ 2. Learn how to determine whether this sequence is arithmetic, geometric, or neither, and calculate the first five terms. Suitable for Grades 8-10.

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