Find the sum of the arithmetic sequence 3, 5, ..., 23.

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Multiple Choice

Find the sum of the arithmetic sequence 3, 5, ..., 23.

Explanation:
For an arithmetic sequence, the sum of the first n terms is S_n = n/2 times (first term plus last term). Here the first term is 3 and the last term is 23, with common difference 2. First find how many terms there are: a_n = a1 + (n−1)d → 23 = 3 + (n−1)·2 → 23 = 3 + 2n − 2 → 23 = 2n + 1 → n = 11. Now compute the sum: S_11 = 11/2 × (3 + 23) = 11/2 × 26 = 11 × 13 = 143. The sum is 143, which is the correct value.

For an arithmetic sequence, the sum of the first n terms is S_n = n/2 times (first term plus last term). Here the first term is 3 and the last term is 23, with common difference 2. First find how many terms there are: a_n = a1 + (n−1)d → 23 = 3 + (n−1)·2 → 23 = 3 + 2n − 2 → 23 = 2n + 1 → n = 11. Now compute the sum: S_11 = 11/2 × (3 + 23) = 11/2 × 26 = 11 × 13 = 143. The sum is 143, which is the correct value.

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