To find the rule for the pattern sequence, let’s examine the number of dots in each pattern and observe any increments.

Analysis of Each Pattern:

1. Pattern 1: 5 dots
2. Pattern 2: 7 dots
3. Pattern 3: 9 dots
4. Pattern 4: 11 dots

Observing the Pattern:

Each new pattern adds 2 dots to the previous one.

Conclusion for the Rule:

1. Start with: 5 dots
2. Add: 2 dots each time

Thus, the rule for this sequence is:

• Start with 5 dots, and add 2 dots each time.

Would you like further explanation on how to find or apply rules in sequences?

Additional Questions:

1. What would the 5th pattern look like based on this rule?
2. How do we represent this sequence using an algebraic formula?
3. Can we create a general formula for the $n$-th term in this sequence?
4. How many dots will there be in the 10th pattern?
5. If the sequence continued indefinitely, would the pattern always increase linearly?

Tip:

When finding a sequence rule, observe the differences between terms to identify if it’s an arithmetic (constant addition/subtraction) or geometric (constant multiplication/division) sequence.