calculate the next four terms for the sequence 10, 5, 2,1,¼,⅝....

The given sequence is \(10, 5, 2, 1, \frac{1}{4}, \frac{1}{8}, \ldots\).

To determine the next four terms, we should first identify the pattern in the sequence. Notice that each term is obtained by dividing the previous term by a certain number:

1. \( \frac{10}{2} = 5 \)
2. \( \frac{5}{2.5} = 2 \)
3. \( \frac{2}{2} = 1 \)
4. \( \frac{1}{4} = \frac{1}{4} \)
5. \( \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} \)

The sequence suggests that each term after the first is obtained by dividing the previous term by the number that increases in sequence.

Continuing this pattern:

6. \( \frac{1}{8} \times \frac{1}{2} = \frac{1}{16} \)
7. \( \frac{1}{16} \times \frac{1}{2} = \frac{1}{32} \)
8. \( \frac{1}{32} \times \frac{1}{2} = \frac{1}{64} \)
9. \( \frac{1}{64} \times \frac{1}{2} = \frac{1}{128} \)

So, the next four terms in the sequence are:

- \( \frac{1}{16} \)
- \( \frac{1}{32} \)
- \( \frac{1}{64} \)
- \( \frac{1}{128} \)

Would you like any details on how the pattern is derived, or do you have any questions?

Here are 5 related questions you might find interesting:
1. How can you express this sequence as a general formula?
2. What would the sequence look like if the initial term were different?
3. How does this sequence compare to geometric sequences?
4. What is the sum of this sequence as it approaches infinity?
5. Can you identify a real-world application where this sequence might appear?

**Tip:** When identifying sequences, look for a pattern in how the terms change relative to one another (e.g., multiplication, division, addition).

Explore how to calculate the next four terms in the sequence 10, 5, 2, 1, ¼, ⅝... through division patterns. Understand the sequence's geometric nature and learn how each term is derived from the previous one. Suitable for Grades 9-12.

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