Final answer:
To find the 8th term of the geometric sequence 6, -12, 24, ..., use the formula an = a1 * r(n-1) where an is the nth term, a1 is the first term, and r is the common ratio. Plugging in the values, the 8th term is -768.
Step-by-step explanation:
To find the 8th term of the geometric sequence 6, -12, 24, ..., you need to determine the common ratio. The common ratio is found by dividing any term by the previous term. For example, -12 / 6 = -2, and 24 / -12 = -2. So, the common ratio is -2. To find the 8th term, you can use the formula:
an = a1 * r(n-1)
where an is the nth term, a1 is the first term, and r is the common ratio. Plugging in the values, you get:
a8 = 6 * (-2)(8-1)
a8 = 6 * (-2)7
a8 = 6 * (-128)
a8 = -768