Answer:
The 12th term of the geometric sequence 2, -8, 32, ... is -8,388,608.
Explanation:
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant factor. In this case, the constant factor can be found by dividing any term by the previous term:
-8 / 2 = -4
32 / -8 = -4
So the constant factor, or the common ratio (r), is -4.
The general formula for finding the nth term of a geometric sequence is:
an = a1 * r^(n-1)
where an is the nth term, a1 is the first term, r is the common ratio, and n is the position of the term in the sequence.
We want to find the 12th term (a12), so n = 12. The first term (a1) is 2, and the common ratio (r) is -4:
a12 = 2 * (-4)^(12-1)
a12 = 2 * (-4)^11
Now calculate the value:
a12 = 2 * (-4194304)
a12 = -8388608