https://file.aiquickdraw.com/mathbot/file/1726700826468gmkd9rxp.jpg

Let's work through each of these problems from the image:

### 17) Sequence: -4, -3, -7/2, -5/2, -3, ?
To determine the next number, we need to find the pattern of differences between consecutive terms:
- \(-3 - (-4) = 1\)
- \(-\frac{7}{2} - (-3) = \frac{-7 + 6}{2} = \frac{-1}{2}\)
- \(-\frac{5}{2} - (-\frac{7}{2}) = \frac{-5 + 7}{2} = 1\)
- \(-3 - (-\frac{5}{2}) = \frac{-6 + 5}{2} = \frac{-1}{2}\)

The pattern alternates between \(+1\) and \(-\frac{1}{2}\). Following this, the next step is \(+1\), so the next number after \(-3\) will be \(-\frac{3}{2}\).

Answer: **A. \(-\frac{3}{2}\)**

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### 18) Sequence: \(\frac{5}{4}, \frac{1}{4}, \frac{3}{4}, -\frac{1}{4}, \frac{1}{4}, ?\)
The pattern seems to alternate with fractional changes:
- \(\frac{1}{4} - \frac{5}{4} = -1\)
- \(\frac{3}{4} - \frac{1}{4} = +\frac{1}{2}\)
- \(-\frac{1}{4} - \frac{3}{4} = -1\)
- \(\frac{1}{4} - (-\frac{1}{4}) = +\frac{1}{2}\)

The changes alternate between \(-1\) and \(+\frac{1}{2}\). Following this, the next change is \(-1\), so the next number is \(\frac{1}{4} - 1 = -\frac{3}{4}\).

Answer: **D. \(-\frac{3}{4}\)**

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### 19) Sequence: \(-2, -4, 2, 4, 10, ?\)
Let's look at the pattern:
- \(-4 - (-2) = -2\)
- \(2 - (-4) = 6\)
- \(4 - 2 = 2\)
- \(10 - 4 = 6\)

The differences alternate between \(-2\) and \(+6\). Following this, the next difference should be \(+2\), so the next number is \(10 + 6 = 16\).

Answer: **D. 16**

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### 20) Sequence: \(8, 4, 5, \frac{5}{2}, \frac{7}{2}, ?\)
This sequence seems to decrease and then increase with fractions:
- \(4 - 8 = -4\)
- \(5 - 4 = 1\)
- \(\frac{5}{2} - 5 = -\frac{5}{2}\)
- \(\frac{7}{2} - \frac{5}{2} = 1\)

The pattern alternates: \(-4, +1, -\frac{5}{2}, +1\). The next step should be \(-\frac{5}{2}\), so the next number is \(\frac{7}{2} + 1 = \frac{9}{2}\).

Answer: **C. \(\frac{9}{2}\)**

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Let me know if you want further details or clarification on any step.

Here are five related questions:
1. How do you identify patterns in a sequence of numbers?
2. What are common types of numerical sequences (arithmetic, geometric, etc.)?
3. How can alternating patterns affect predictions in a sequence?
4. What is the method for finding the next term in a sequence with fractions?
5. How do differences between terms help in identifying patterns?

**Tip:** Always check if the differences or ratios between consecutive terms follow a predictable pattern when solving sequence problems.

Based on the sequences shown in the image, find the next term for each sequence and select the correct answer from the options.

Learn how to solve sequence problems by identifying arithmetic and alternating patterns. This example includes sequences with both integers and fractions. Suitable for students in Grades 9-12.

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