There is a certain sequence of positive real numbers. Beginning from the third term, each term of the sequence is the sum of all the previous terms. The seventh term is equal to `1000` and the first term is equal to `1`. The second term of this sequence is equal to

Options

A. `246`
B. `(123)/(2)`
C. `(123)/(4)`
D. `124`

Explanation

To solve the problem step by step, we will denote the terms of the sequence as follows:

- Let \( T_1 \) be the first term.
- Let \( T_2 \) be the second term.
- Let \( T_3 \) be the third term.
- Let \( T_4 \) be the fourth term.
- Let \( T_5 \) be the fifth term.
- Let \( T_6 \) be the sixth term.
- Let \( T_7 \) be the seventh term.

Given:
- \( T_1 = 1 \)
- \( T_7 = 1000 \)

From the problem statement, we know that starting from the third term, each term is the sum of all previous terms:
- \( T_3 = T_1 + T_2 \)
- \( T_4 = T_1 + T_2 + T_3 \)
- \( T_5 = T_1 + T_2 + T_3 + T_4 \)
- \( T_6 = T_1 + T_2 + T_3 + T_4 + T_5 \)
- \( T_7 = T_1 + T_2 + T_3 + T_4 + T_5 + T_6 \)

### Step 1: Express each term in terms of \( T_1 \) and \( T_2 \)

1. **Calculate \( T_3 \)**:
\[ T_3 = T_1 + T_2 = 1 + T_2 \]

2. **Calculate \( T_4 \)**:
\[ T_4 = T_1 + T_2 + T_3 = 1 + T_2 + (1 + T_2) = 2 + 2T_2 \]

3. **Calculate \( T_5 \)**:
\[ T_5 = T_1 + T_2 + T_3 + T_4 = 1 + T_2 + (1 + T_2) + (2 + 2T_2) = 4 + 4T_2 \]

4. **Calculate \( T_6 \)**:
\[ T_6 = T_1 + T_2 + T_3 + T_4 + T_5 = 1 + T_2 + (1 + T_2) + (2 + 2T_2) + (4 + 4T_2) = 8 + 8T_2 \]

5. **Calculate \( T_7 \)**:
\[ T_7 = T_1 + T_2 + T_3 + T_4 + T_5 + T_6 = 1 + T_2 + (1 + T_2) + (2 + 2T_2) + (4 + 4T_2) + (8 + 8T_2) = 16 + 16T_2 \]

### Step 2: Set up the equation for \( T_7 \)

Since we know \( T_7 = 1000 \), we can set up the equation:
\[ 16 + 16T_2 = 1000 \]

### Step 3: Solve for \( T_2 \)

1. Subtract 16 from both sides:
\[ 16T_2 = 1000 - 16 \]
\[ 16T_2 = 984 \]

2. Divide both sides by 16:
\[ T_2 = \frac{984}{16} = 61.5 \]

### Conclusion

Thus, the second term of the sequence is:
\[ \boxed{61.5} \]