If `P(n)` is the statement `"2^(3n)-1` . Is an integral multiple `7",` and if `P(r)` is true, prove that `P(r+1)` is true.

Explanation

To prove that if \( P(r) \) is true, then \( P(r+1) \) is also true, we will use the principle of mathematical induction.

### Step-by-Step Solution:

1. **Base Case**:
We need to first establish that \( P(1) \) is true.
\[
P(1): 2^{3 \cdot 1} - 1 = 2^3 - 1 = 8 - 1 = 7
...