Let’s solve the problem based on the rules provided in the image:

Rules:

• Start with 2 counters.
• Add 4 counters each time for the next pattern.

Sequence Pattern:

The sequence for the number of counters is arithmetic, where the first term $a = 2$, and the common difference $d = 4$.

The formula for the $n$-th term of an arithmetic sequence is: $a_n = a + (n-1) \cdot d$

For the 4th Pattern ($n = 4$):

$a_4 = 2 + (4-1) \cdot 4 = 2 + 12 = 14$

For the 5th Pattern ($n = 5$):

$a_5 = 2 + (5-1) \cdot 4 = 2 + 16 = 18$

For the 6th Pattern ($n = 6$):

$a_6 = 2 + (6-1) \cdot 4 = 2 + 20 = 22$

Final Answer:

• 4th Pattern: 14 counters
• 5th Pattern: 18 counters
• 6th Pattern: 22 counters

Would you like a step-by-step explanation or have any additional questions?

Expanding your knowledge:

1. What is the 10th term in this sequence?
2. How do you derive the sum of the first 6 patterns?
3. What if you start with 3 counters and add 5 counters each time?
4. How is an arithmetic sequence different from a geometric sequence?
5. Can you calculate the position ($n$) if the number of counters is 50?

Tip:

For arithmetic sequences, always identify the first term and the common difference—they are key to solving any problem!