Final answer:
To find the maximum sum of an arithmetic sequence, we need to find the common difference and the number of terms in the sequence. Then we can use the formula for the sum of an arithmetic sequence to calculate the maximum sum. In this case, the maximum sum of the arithmetic sequence with a second term of twenty-eight and a fourth term of twenty is sixty.
Step-by-step explanation:
To find the maximum sum of an arithmetic sequence, we need to find the common difference and the number of terms in the sequence. Then we can use the formula for the sum of an arithmetic sequence to calculate the maximum sum.
1. Identify the common difference, which is the difference between consecutive terms. In this case, the common difference is 21 - 17 = 4.
2. Find the number of terms in the sequence. Here, we are given the second term and the fourth term. So, we know that the sequence has at least 4 terms.
3. To maximize the sum, we want the sequence to include as many terms as possible. We can calculate the maximum number of terms using the formula: maximum number of terms = (last term - first term) / common difference + 1. Since the last term is 20 and the common difference is 4, the maximum number of terms is (20 - 17) / 4 + 1 = 2.
4. Now, we can calculate the maximum sum using the formula: maximum sum = (number of terms / 2) * (2 * second term + (number of terms - 1) * common difference). Plugging in the values, we get (2 / 2) * (2 * 28 + (2 - 1) * 4) = 1 * (56 + 4) = 60.
Therefore, the maximum sum of the arithmetic sequence is 60.