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)= 2n`

Answer

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

### Step-by-Step Solution:

1. **Calculate the first term \( a_1 \)**:
\[ a_1 = 2 \times 1 = 2 \]

2. **Calculate the second term \( a_2 \)**:
\[ a_2 = 2 \times 2 = 4 \]

3. **Calculate the third term \( a_3 \)**:
\[ a_3 = 2 \times 3 = 6 \]

4. **Calculate the fourth term \( a_4 \)**:
\[ a_4 = 2 \times 4 = 8 \]

5. **Calculate the fifth term \( a_5 \)**:
\[ a_5 = 2 \times 5 = 10 \]

### Summary of the First Five Terms:
The first five terms of the sequence are:
\[ a_1 = 2, \quad a_2 = 4, \quad a_3 = 6, \quad a_4 = 8, \quad a_5 = 10 \]

Thus, the sequence is:
\[ 2, 4, 6, 8, 10 \]