An arithmetic sequence has a first term of 1, a last term of 81, and 9 is also in the sequence. Let the number of terms in this sequence be $n$, where $n \leq 100$ . Select the correct options.\\
(1) $n$ is odd\\
(2) 41 must be in this arithmetic sequence\\
(3) The common difference of all arithmetic sequences satisfying the conditions is an integer\\
(4) There are 10 arithmetic sequences satisfying the conditions\\
(5) If $n$ is a multiple of 7, then $n = 21$