Pattern 1 has 4 dots, pattern 2 has 7 dots, pattern 3 has 10 dots. How many dots in pattern 4

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.

Pattern 1 has 4 dots, pattern 2 has 7 dots, pattern 3 has 10 dots. How many dots in pattern 4?

Learn how to solve the problem of determining the number of dots in a pattern following an arithmetic progression. Given the patterns with 4, 7, and 10 dots, use the formula for an arithmetic sequence to calculate the dots in pattern 4. Suitable for students in Grades 6-8.

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