To determine whether the given sequence is arithmetic, geometric, or neither, we analyze the sequence:
$0.3, -3, 30, -300, 3000, \dots$

Step 1: Check for an arithmetic sequence

An arithmetic sequence has a constant common difference $d$, which is obtained by subtracting consecutive terms:
$d = a_{n+1} - a_n$

Let’s calculate the differences:

1. $-3 - 0.3 = -3.3$
2. $30 - (-3) = 33$
3. $-300 - 30 = -330$
4. $3000 - (-300) = 3300$

The differences are clearly not constant ($-3.3$, $33$, $-330$, $3300$).
Thus, the sequence is not arithmetic.

Step 2: Check for a geometric sequence

A geometric sequence has a constant common ratio $r$, which is obtained by dividing consecutive terms:
$r = \frac{a_{n+1}}{a_n}$

Let’s calculate the ratios:

1. $\frac{-3}{0.3} = -10$
2. $\frac{30}{-3} = -10$
3. $\frac{-300}{30} = -10$
4. $\frac{3000}{-300} = -10$

The ratios are all constant and equal to $-10$.
Thus, the sequence is geometric with a common ratio of $r = -10$.

Final Answer:

The sequence is geometric, and the common ratio is $-10$.

Do you want more details or have any questions?

Here are 5 related questions you may find interesting:

1. How do you distinguish between arithmetic and geometric sequences?
2. What is the formula for the $n$-th term of a geometric sequence?
3. How can you calculate the sum of a geometric sequence?
4. What happens if the common ratio $r$ is between $-1$ and $1$?
5. Can a sequence be both arithmetic and geometric?

Tip: In a geometric sequence, the ratio between any two consecutive terms is always the same!