Answer: Let the common ratio of the exponential sequence be denoted by r. Then, the 10th term of the sequence can be expressed as:
a10 = ar^9
We also know that the first term of the sequence is 1, so:
a1 = ar^0 = a = 1
We can use these equations to solve for r. First, we can substitute a10 = -512 and a = 1:
-512 = 1 * r^9
Simplifying:
r^9 = -512
Taking the ninth root of both sides:
r = -2
Therefore, the common ratio of the exponential sequence is -2.
Explanation: