The first term of an arithmetic sequence is \(a\) and the common difference is \(d\).

The sum of the first \(n\) terms is denoted by \(S_n\).

If \(S_8>3S_6\), what can be deduced about the sign of \(a\) and the sign of \(d\)?

both \(a\) and \(d\) are negative

\(a\) is positive, \(d\) is negative

\(a\) is negative, \(d\) is positive

\(a\) is negative, but the sign of \(d\) cannot be deduced

\(d\) is negative, but the sign of \(a\) cannot be deduced

neither the sign of \(a\) nor the sign of \(d\) can be deduced

*[Choose the one correct answer and explain your reasoning.]*