To solve the problem:

Given Information:

1. Start with 3 counters in the 1st pattern.
2. Add 4 counters for each subsequent pattern.

Step-by-Step Solution:

• General formula: The number of counters for the $n$-th pattern is given by:
  $\text{Counters} = 3 + 4(n-1)$ where $n$ is the pattern number.

• 4th Pattern:
  Substituting $n = 4$:
  $\text{Counters} = 3 + 4(4-1) = 3 + 4 \cdot 3 = 3 + 12 = 15$

• 5th Pattern:
  Substituting $n = 5$:
  $\text{Counters} = 3 + 4(5-1) = 3 + 4 \cdot 4 = 3 + 16 = 19$

• 6th Pattern:
  Substituting $n = 6$:
  $\text{Counters} = 3 + 4(6-1) = 3 + 4 \cdot 5 = 3 + 20 = 23$

Final Answer:

• 4th Pattern: 15 counters
• 5th Pattern: 19 counters
• 6th Pattern: 23 counters

Would you like further explanations or examples?

Related Questions:

1. How would the formula change if we started with a different number of counters, like 5?
2. What is the 10th pattern's total number of counters?
3. How can we write this sequence as an arithmetic progression?
4. What is the sum of the counters in the first 6 patterns?
5. Can this sequence be visualized on a graph, and what would it look like?

Tip:

For sequences, always look for the starting value and the common difference (or change). This forms the basis of the arithmetic sequence formula!