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. $-\frac{3}{2}$

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. $-\frac{3}{4}$

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

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. $\frac{9}{2}$

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.