The sequence in the image is:

$4, 4, 2, 5, 20, 4, 10, \ldots$

We need to determine the next number in the sequence.

Step-by-step Analysis

Let's look for patterns:

1. First Segment: The first three numbers are $4, 4, 2$. These don't show a clear arithmetic or geometric progression.

2. Second Segment: The numbers $5, 20$ follow. If we observe, $20 = 5 \times 4$. This suggests some form of multiplication might be at play here.

3. Third Segment: Then the sequence continues as $4, 10$. We see that $10 = 4 \times 2.5$.

Finding the Pattern

The sequence seems to alternate between certain operations. One possibility is that it multiplies by a number that varies each time. Let's investigate further:

• $4 \rightarrow 4$: No change.
• $4 \rightarrow 2$: Divides by 2.
• $2 \rightarrow 5$: Adds 3.
• $5 \rightarrow 20$: Multiplies by 4.
• $20 \rightarrow 4$: Divides by 5.
• $4 \rightarrow 10$: Multiplies by 2.5.

Determining the Next Number

If the pattern continues, we expect the sequence to alternate between operations. Following the pattern:

1. After multiplying by 2.5 (10): The next operation should be similar to earlier operations where we divide.

2. Dividing $10$ by $2$: $10 \div 2 = 5$

Thus, the next number in the sequence is 5.

Answer:

The correct choice is:

$\boxed{5}$

Would you like further details or have any questions?

Related Questions

1. What would be the next number if the sequence continued further?
2. How would the sequence change if a different operation was applied after the second segment?
3. Can this sequence be modeled using a mathematical formula or function?
4. What are some other common patterns found in number sequences?
5. How would one recognize arithmetic vs. geometric patterns in sequences?

Tip

When solving number sequences, pay attention to alternating operations; these often indicate a non-linear or composite pattern.