The sequence given is $-6, -3, -1.5, 0.75, \dots$. To determine if the sequence is arithmetic, geometric, or neither:

1. Arithmetic sequence: The difference between consecutive terms is constant.

   • $-3 - (-6) = 3$
   • $-1.5 - (-3) = 1.5$
   • $0.75 - (-1.5) = 2.25$ The differences are not constant, so it is not arithmetic.

2. Geometric sequence: The ratio between consecutive terms is constant.

   • $-3 / -6 = 0.5$
   • $-1.5 / -3 = 0.5$
   • $0.75 / -1.5 = -0.5$ The ratios are not constant ($0.5 \neq -0.5$), so it is not geometric.

Since the sequence is neither arithmetic nor geometric, the correct answer is neither.

Would you like further clarification or have any related questions?

Related Questions:

1. What are the properties of arithmetic sequences?
2. How can we identify a geometric sequence using ratios?
3. Can sequences be both arithmetic and geometric at the same time?
4. What are some examples of sequences that are neither arithmetic nor geometric?
5. How do we define a general formula for non-standard sequences?

Tip:

When analyzing a sequence, always calculate consecutive differences (for arithmetic) and consecutive ratios (for geometric) to identify its nature systematically.