To determine if the sequence $24, 16, 8, \ldots$ is arithmetic or geometric, and to calculate the common difference or ratio:

Step 1: Check for an Arithmetic Sequence

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

• $16 - 24 = -8$
• $8 - 16 = -8$

Since the difference is constant ($-8$), this could be an arithmetic sequence.

Step 2: Check for a Geometric Sequence

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

• $\frac{16}{24} = \frac{2}{3}$
• $\frac{8}{16} = \frac{1}{2}$

The ratio is not constant, so this is not a geometric sequence.

Conclusion

The sequence $24, 16, 8, \ldots$ is arithmetic with a common difference of $-8$.

Would you like further explanation or to explore related concepts?

Follow-Up Questions

1. What is the next term in the sequence $24, 16, 8, \ldots$?
2. How would the sequence differ if it were geometric with a ratio of $\frac{1}{2}$?
3. Can you generalize the $n$-th term of this arithmetic sequence?
4. How would this sequence behave if the common difference were positive instead of negative?
5. What is the sum of the first $n$ terms of this sequence?

Tip

To identify the type of sequence, always verify both the differences (arithmetic) and the ratios (geometric). This ensures no misclassification.