Final answer:
The explicit formula for the given geometric sequence is an = -0.1 × (-0.3)n-1, with the first term being -0.1 and the common ratio being -0.3.
Step-by-step explanation:
The student is asking for the explicit formula for a given geometric sequence. To find the explicit formula, we need to identify the first term (a1) and the common ratio (r) of the sequence. Observing the sequence A. -0.1, B. 0.03, C. -0.009, D. 0.0027, E. -0.00081, we can see that the first term a1 is -0.1, and the common ratio is obtained by dividing any term in the sequence by its preceding term. For example, dividing the second term by the first term, 0.03 / -0.1 = -0.3. Continuing this for other terms confirms that the common ratio r is -0.3. Hence, the explicit formula for the nth term of this geometric sequence is an = a1 × rn-1, which in this case is an = -0.1 × (-0.3)n-1.