No, the sequence \(1, 4, 9, 16\) is not a geometric sequence.

A geometric sequence is one in which each term after the first is found by multiplying the previous term by a constant factor (called the common ratio). For example, in the sequence \(2, 6, 18, 54\), each term is multiplied by 3 to get the next term, so it's a geometric sequence with a common ratio of 3.

In the sequence \(1, 4, 9, 16\), the ratio between consecutive terms is not constant:

- \( \frac{4}{1} = 4 \)
- \( \frac{9}{4} = 2.25 \)
- \( \frac{16}{9} \approx 1.78 \)

Since these ratios are not the same, the sequence is not geometric.

This sequence is actually an arithmetic sequence of squares: \(1^2, 2^2, 3^2, 4^2\).

Would you like more details, or do you have any other questions?

Here are some related questions:
1. What is an arithmetic sequence?
2. How do you identify a geometric sequence?
3. What is the formula for the \(n\)th term in a geometric sequence?
4. Can you explain the difference between arithmetic and geometric sequences?
5. How would you determine the sum of a geometric sequence?

**Tip:** When determining if a sequence is geometric, always check if the ratio between consecutive terms is consistent.

Determine whether the sequence 1, 4, 9, 16 is a geometric sequence. Understand the concepts of geometric and arithmetic sequences, with a detailed explanation of the common ratio and the sequence of squares. Suitable for students in Grades 8-10.

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