It looks like you've uploaded a problem related to a pattern of dots. The problem asks about drawing the next pattern, predicting the number of dots in a future pattern (in this case, pattern 15), and verifying the accuracy of a claim about the number of dots in pattern 20.

Let me break it down for you:

1. Part (a): You need to draw pattern 4 based on the sequence shown.
2. Part (b): You need to find out how many dots there will be in pattern 15, based on the pattern's progression.
3. Part (c): Jack claims that there are 70 dots in pattern 20. You need to verify whether or not this is correct and explain your reasoning.

To assist you effectively, I'll start by identifying the pattern's structure from the given dots in patterns 1, 2, and 3. Then, we'll calculate the number of dots for pattern 15 and check Jack's claim for pattern 20.

Let me first analyze the pattern and continue from there.From the image you uploaded, I can observe the following:

• Pattern 1 has 1 dot.
• Pattern 2 has 3 dots.
• Pattern 3 has 5 dots.

It seems that the pattern is increasing by 2 dots as we progress through each subsequent pattern.

This suggests that the number of dots in pattern $n$ follows a simple arithmetic progression where the first term is 1 (for pattern 1), and the common difference is 2.

General formula:

The number of dots in pattern $n$ can be given by the formula for the nth term of an arithmetic sequence: $a_n = 1 + (n - 1) \times 2$ Simplifying, we get: $a_n = 2n - 1$ Where $a_n$ represents the number of dots in pattern $n$.

Now let's solve the questions:

1. Part (a): Drawing pattern 4: Using the formula, for $n = 4$: $a_4 = 2 \times 4 - 1 = 7$ So, pattern 4 should have 7 dots. You can draw it by placing 7 dots in the same increasing fashion.

2. Part (b): Number of dots in pattern 15: Using the formula for $n = 15$: $a_{15} = 2 \times 15 - 1 = 29$ So, pattern 15 will have 29 dots.

3. Part (c): Jack's claim of 70 dots in pattern 20: For $n = 20$: $a_{20} = 2 \times 20 - 1 = 39$ Therefore, Jack is incorrect. Pattern 20 will have 39 dots, not 70.

Summary:

• Pattern 4 has 7 dots.
• Pattern 15 has 29 dots.
• Pattern 20 has 39 dots (not 70 as Jack claims).

Let me know if you'd like more details or have any further questions!

Related questions to explore:

1. How can we use the formula to find the number of dots in any pattern?
2. How would the pattern change if the number of dots increased by 3 each time?
3. What happens if the first pattern starts with 2 dots instead of 1?
4. Can you explain why the pattern follows an arithmetic progression?
5. How would we graph this sequence of dots?

Tip:

When dealing with patterns, always look for consistent differences between successive terms—this can help you identify if the sequence follows an arithmetic or geometric progression.