Find the sum of the arithmetic sequence with first term 2, common difference 3, and 6 terms.

Find the sum of the arithmetic sequence with first term 2, common difference 3, and 6 terms.

• A. 60
• B. 57
• C. 45
• D. 42

Answer: (B)

Sum of an arithmetic sequence is found by multiplying the number of terms by the average of the first and last terms. Here, the first term is 2, the common difference is 3, and there are 6 terms. The last term is 2 + (6−1)×3 = 17. The average of the first and last terms is (2 + 17)/2 = 9.5. Multiply by the number of terms: 6 × 9.5 = 57. So the sum is 57. The terms are 2, 5, 8, 11, 14, 17, which also add up to 57.

Sum of an arithmetic sequence is found by multiplying the number of terms by the average of the first and last terms. Here, the first term is 2, the common difference is 3, and there are 6 terms. The last term is 2 + (6−1)×3 = 17. The average of the first and last terms is (2 + 17)/2 = 9.5. Multiply by the number of terms: 6 × 9.5 = 57. So the sum is 57. The terms are 2, 5, 8, 11, 14, 17, which also add up to 57.