18. (12 points) Given that all terms of the sequence $\{a_n\}$ are positive numbers, and $S_n$ denotes the sum of the first $n$ terms of $\{a_n\}$. Choose two of the following three statements as conditions and prove the remaining one.\\
(1) The sequence $\{a_n\}$ is an arithmetic sequence;\\
(2) The sequence $\{\sqrt{S_n}\}$ is an arithmetic sequence;\\
(3) $a_2 = 3a_1$.
Note: If different combinations are answered correctly, only the first answer will be scored.