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)=3n-2 `

Answer

To find the first five terms of the sequence defined by the rule \( a_n = 3n - 2 \), we will substitute the values of \( n \) from 1 to 5 into the formula.

### Step-by-Step Solution:

1. **Calculate \( a_1 \)**:
\[ a_1 = 3(1) - 2 = 3 - 2 = 1 \]
So, the first term \( a_1 \) is 1.

2. **Calculate \( a_2 \)**:
\[ a_2 = 3(2) - 2 = 6 - 2 = 4 \]
So, the second term \( a_2 \) is 4.

3. **Calculate \( a_3 \)**:
\[ a_3 = 3(3) - 2 = 9 - 2 = 7 \]
So, the third term \( a_3 \) is 7.

4. **Calculate \( a_4 \)**:
\[ a_4 = 3(4) - 2 = 12 - 2 = 10 \]
So, the fourth term \( a_4 \) is 10.

5. **Calculate \( a_5 \)**:
\[ a_5 = 3(5) - 2 = 15 - 2 = 13 \]
So, the fifth term \( a_5 \) is 13.

### Conclusion:
The first five terms of the sequence are:
\[ 1, 4, 7, 10, 13 \]