Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
A pattern of letter A as `A`

Answer

To find the rule for the number of matchsticks required to create the letter "A" using matchsticks, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Structure of the Letter "A":**
The letter "A" can be visualized as consisting of three matchsticks. Two matchsticks form the sides of the "A" and one matchstick forms the crossbar in the middle.

2. **Count the Matchsticks for One "A":**
- For one letter "A", we need a total of 3 matchsticks.
- Therefore, we can say:
\[ \text{Matchsticks for 1 A} = 3 \]

3. **Establish a Variable for the Number of Letters:**
- Let \( n \) represent the number of letters "A" we want to create.
- The total number of matchsticks required for \( n \) letters "A" would be the number of matchsticks for one "A" multiplied by \( n \).

4. **Write the Rule Using the Variable:**
- The formula for the total number of matchsticks needed can be expressed as:
\[ \text{Total Matchsticks} = 3n \]
- Here, \( 3n \) indicates that for each letter "A", 3 matchsticks are needed.

5. **Examples:**
- If \( n = 1 \) (1 letter A), then matchsticks needed = \( 3 \times 1 = 3 \).
- If \( n = 2 \) (2 letters A), then matchsticks needed = \( 3 \times 2 = 6 \).
- If \( n = 3 \) (3 letters A), then matchsticks needed = \( 3 \times 3 = 9 \).
- If \( n = 4 \) (4 letters A), then matchsticks needed = \( 3 \times 4 = 12 \).

### Final Rule:
The rule that gives the number of matchsticks required to make \( n \) letters "A" is:
\[ \text{Total Matchsticks} = 3n \]