- In a geometric sequence, the \( n \)-th term can be represented as:
\[ a_n = a_1 \cdot r^{(n-1)} \]
where:
- \( a_n \) is the \( n \)-th term,
- \( a_1 \) is the first term,
- \( r \) is the common ratio,
- \( n \) is the term number.
For this situation, the first term \( a_1 = 6 \) and the common ratio \( r = -8 \). Therefore, the equation for the \( n \)-th term of the sequence is:
\[ a_n = 6 \cdot (-8)^{(n-1)} \]
- To find the 7th term of the sequence \( a_7 \):
\[ a_7 = 6 \cdot (-8)^{(7-1)} = 6 \cdot (-8)^6 \]
Now, we calculate \( (-8)^6 \):
\[ (-8)^6 = 262144 \]
So,
\[ a_7 = 6 \cdot 262144 = 1572864 \]
Thus, the 7th term of the sequence is:
\[ \boxed{1572864} \]