The first term of an arithmetic progression is and its common difference is . What is the sum of its first terms?

Answer and explanation

Correct answer: A. 690

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  1. Step 1: The sum of the first terms of an arithmetic progression is given by the formula , where is the first term and is the common difference.
  2. Step 2: Substitute , , and : .
  3. Step 3: Simplify inside brackets: . Multiply: .
Answer
690.
Why not the others: '684' evaluates the summation using terms instead of ; '1410' omits the factor of in the series formula; '705' adds rather than subtracts the common difference term.

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