Write the first five terms of the sequence using the given rule. In each case, the initial value of the index is 1.
`a_(n) `= nth prime number for all natural numbers n .

Answer

To find the first five terms of the sequence defined by \( a_n = \) nth prime number, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Sequence Rule**: The sequence is defined such that \( a_n \) represents the nth prime number.

2. **Define Prime Numbers**: Recall that prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. The first few prime numbers are: 2, 3, 5, 7, 11, 13, ...

3. **Calculate Each Term**:
- **For \( n = 1 \)**:
- The first prime number is **2**.
- So, \( a_1 = 2 \).
- **For \( n = 2 \)**:
- The second prime number is **3**.
- So, \( a_2 = 3 \).
- **For \( n = 3 \)**:
- The third prime number is **5**.
- So, \( a_3 = 5 \).
- **For \( n = 4 \)**:
- The fourth prime number is **7**.
- So, \( a_4 = 7 \).
- **For \( n = 5 \)**:
- The fifth prime number is **11**.
- So, \( a_5 = 11 \).

4. **Compile the Results**: The first five terms of the sequence are:
\[ a_1, a_2, a_3, a_4, a_5 = 2, 3, 5, 7, 11 \]

### Final Answer:
The first five terms of the sequence are: **2, 3, 5, 7, 11**.

---