In an arithmetic sequence, the difference between consecutive terms is constant.
To find the common difference (\(d\)), we can subtract the first term from the second term:
\[ d = 5 - 9 = -4 \]
We can also verify this with the next terms:
\[ 1 - 5 = -4 \] \[ -3 - 1 = -4 \]
Now that we have the common difference \(d = -4\), we can find the \(n\)-th term of the sequence using the formula:
\[ a_n = a_1 + (n-1) \cdot d \]
where \(a_1\) is the first term, and \(n\) is the term number. In this case, \(a_1 = 9\).
To find the 6th term (\(a_6\)):
\[ a_6 = a_1 + (6-1) \cdot d \] \[ a_6 = 9 + (5) \cdot (-4) \] \[ a_6 = 9 - 20 \] \[ a_6 = -11 \]
So, the \(6\)th term \(a_6\) is \(\boxed{-11}\).
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