To solve this problem, let's analyze the pattern progression:

1. Identify the Pattern's Structure:

   • In the first pattern, there are 6 dots.
   • In the second pattern, there are 10 dots.
   • In the third pattern, there are 14 dots.

2. Determine the Difference:

   • Between the first and second patterns, 4 dots are added (10 - 6 = 4).
   • Between the second and third patterns, 4 dots are also added (14 - 10 = 4).
   • This consistent increase suggests an arithmetic sequence where each term adds 4 dots.

3. Formulate the Sequence:

   • The sequence starts with 6 dots and increases by 4 dots each step. The general formula for the $n$-th term of an arithmetic sequence is: $a_n = a_1 + (n - 1) \times d$ where:
   • $a_1$ is the first term (6 dots),
   • $d$ is the common difference (4 dots),
   • $n$ is the term number we want to find (12th term in this case).

4. Calculate the 12th Term: $a_{12} = 6 + (12 - 1) \times 4$ $a_{12} = 6 + 11 \times 4$ $a_{12} = 6 + 44$ $a_{12} = 50$

Therefore, the 12th pattern will contain 50 dots.

Would you like further details or have any questions?

Here are five related questions you might find useful:

1. How do we recognize arithmetic sequences in different types of patterns?
2. What is the difference between arithmetic and geometric sequences?
3. How can we derive the general formula for the $n$-th term in an arithmetic sequence?
4. What are common applications of arithmetic sequences in real-life scenarios?
5. How do we determine the sum of the first $n$ terms in an arithmetic sequence?

Tip: Always check for a common difference in sequences to quickly identify if it's arithmetic, which makes solving much easier.