Final answer:
The explicit formula for the geometric sequence 2, 10, 50, 250, 1250 with a constant multiplier of 5 is given by a_n = 2 x 5^(n-1), where n represents the term number.
Step-by-step explanation:
The sequence 2, 10, 50, 250, 1250 is an example of a geometric sequence where each term is multiplied by a constant to get the next term. In this case, the constant is 5. We can express the n-th term of a geometric sequence as an = a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number.
For this sequence, the first term a1 is 2 and the common ratio r is 5. Therefore, the explicit formula for the n-th term is an = 2 × 5(n-1).