What is the sum of the odd numbers from 1 through 179?

• A. 8,000
• B. 7,900
• C. 8,500
• D. 8,100

Answer: (D)

Odd numbers from 1 to 179 form an arithmetic sequence with a common difference of 2. There are 90 terms because (179 − 1)/2 + 1 = 90. The sum of an arithmetic sequence is (first + last)/2 × number of terms, so the average of the ends is (1 + 179)/2 = 90, and there are 90 terms. Multiply: 90 × 90 = 8100. Equivalently, the sum of the first n odd numbers is n^2, with n = 90, giving 8100. Therefore, the sum is 8,100.