Answer :
Final answer:
To calculate S₇₅ for the arithmetic sequence defined by {An} = {67-2n}, the sum of the first 75 terms is -1,350.
Explanation:
To calculate S₇₅ for the arithmetic sequence defined by {An} = {67-2n}, we need to find the sum of the first 75 terms. The formula for the sum of an arithmetic sequence is Sₙ = (n/2)(a₁ + aₙ), where Sₙ is the sum of the first n terms, a₁ is the first term, and aₙ is the nth term. In this case, a₁ = 67-2(1) = 65 and aₙ = 67-2(75) = -133. Plugging these values into the formula, we get S₇₅ = (75/2)(65 + (-133)) = (75/2)(-68) = -1,350.
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