We observe that the number of dots in each pattern follows a sequence:

• Pattern 1 has 4 dots.
• Pattern 2 has 7 dots.
• Pattern 3 has 10 dots.

We can see that the difference between consecutive patterns is constant:

• $7 - 4 = 3$
• $10 - 7 = 3$

This suggests that the sequence follows an arithmetic progression, where the common difference $d = 3$.

To find the number of dots in pattern 4, we can use the formula for the $n$-th term of an arithmetic sequence:

$a_n = a_1 + (n - 1) \cdot d$

Where:

• $a_1$ is the first term (4 dots),
• $d$ is the common difference (3),
• $n$ is the pattern number (in this case, 4).

Substitute the values into the formula:

$a_4 = 4 + (4 - 1) \cdot 3 = 4 + 3 \cdot 3 = 4 + 9 = 13$

So, pattern 4 has 13 dots.

Would you like further clarification or more examples?

Related Questions:

1. What would the 5th pattern have in terms of dots?
2. How can you calculate the total number of dots in the first 5 patterns?
3. What is the general formula for the number of dots in pattern $n$?
4. If the difference between patterns were 2 instead of 3, how would the sequence change?
5. Can we apply this to other sequences with different starting numbers or differences?

Tip: In any arithmetic sequence, the difference between consecutive terms is always constant. This is key to predicting future terms or finding the total sum of terms.