The sequence given in the question is:
400, 40, 4, ...

We need to determine if the sequence is arithmetic or geometric, and find the common difference (if arithmetic) or the common ratio (if geometric).

Step 1: Check if it is Arithmetic

An arithmetic sequence has a constant difference between consecutive terms.
Let’s calculate the differences:

• $40 - 400 = -360$
• $4 - 40 = -36$

Since the differences are not constant, this is not an arithmetic sequence.

Step 2: Check if it is Geometric

A geometric sequence has a constant ratio between consecutive terms.
Let’s calculate the ratios:

• $\frac{40}{400} = 0.1$
• $\frac{4}{40} = 0.1$

The ratio is constant ($0.1$), so this is a geometric sequence.

Step 3: Write the Answer

The sequence is geometric, and the common ratio is $0.1$ (in simplest form).

Let me know if you need further clarification or details!

Related Questions:

1. How do you determine if a sequence is arithmetic?
2. What are some real-life examples of geometric sequences?
3. How would you describe the formula for the nth term of a geometric sequence?
4. How do arithmetic and geometric sequences differ in behavior over time?
5. Can a sequence be neither arithmetic nor geometric?

Tip:

For a geometric sequence, divide any term by the previous term to find the common ratio. Always double-check consistency across terms!