Final answer:
The explicit formula for the given arithmetic sequence is an = 20 - 57(n - 1), which is option (B). This is determined by finding the common difference between consecutive terms and applying it to the general formula for an arithmetic sequence.
Step-by-step explanation:
The student is asking for the explicit formula for an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the previous term. To find the explicit formula, we can use the first two terms of the sequence. The second term (-37) is obtained by adding the common difference to the first term (20). To find this common difference, we subtract the first term from the second term: -37 - 20 = -57. Therefore, the common difference is -57.
The general explicit formula for an arithmetic sequence is an = a1 + d(n - 1), where a1 is the first term and d is the common difference. Substituting the given values, the explicit formula becomes an = 20 - 57(n - 1). Thus, the correct answer is (B) an = 20 - 57(n - 1).