Final answer:
The explicit formula for the geometric sequence 10, -30, 90, -270 is an = 10 × (-3)^(n-1), where n is the term number.
Step-by-step explanation:
The explicit formula for a geometric sequence can be expressed as an = a1 × r(n-1), where an is the n-th term of the sequence, a1 is the first term, r is the common ratio, and n is the term number. For the sequence 10, -30, 90, -270, the first term a1 is 10, and the common ratio r is -3 (since each term is -3 times the preceding term). The explicit formula for this sequence is therefore an = 10 × (-3)(n-1).