To find the sixth term \( a_6 \) of the arithmetic sequence given, we first need to identify the common difference \( d \) of the sequence.
The first four terms are:
- \( a_1 = 9 \)
- \( a_2 = 5 \)
- \( a_3 = 1 \)
- \( a_4 = -3 \)
Now, we calculate the common difference \( d \): \[ d = a_2 - a_1 = 5 - 9 = -4 \] \[ d = a_3 - a_2 = 1 - 5 = -4 \] \[ d = a_4 - a_3 = -3 - 1 = -4 \]
Since the common difference \( d \) is consistent at \( -4 \), we can use this to find the subsequent terms.
We can use the formula for the \( n \)-th term of an arithmetic sequence: \[ a_n = a_1 + (n - 1) d \]
We need to find the sixth term \( a_6 \): \[ a_6 = a_1 + (6 - 1) d = 9 + 5(-4) \] \[ a_6 = 9 + 5(-4) = 9 - 20 = -11 \]
Thus, the sixth term \( a_6 \) is: \[ \boxed{-11} \]