To calculate the 50th upper partial sum (denoted as \( S_{50} \)) of the arithmetic sequence given by \( a_n = 71 - 2.3n \), we first need to determine the first term (\( a_1 \)), the 50th term (\( a_{50} \)), and the number of terms in the sequence.
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Find the first term \( a_1 \): \[ a_1 = 71 - 2.3(1) = 71 - 2.3 = 68.7 \]
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Find the 50th term \( a_{50} \): \[ a_{50} = 71 - 2.3(50) = 71 - 115 = -44 \]
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Determine the number of terms and the common difference \( d \): The common difference \( d \) of the sequence can be found by calculating the difference between consecutive terms: \[ d = a_{n+1} - a_n = (71 - 2.3(n+1)) - (71 - 2.3n) = -2.3 \]
The number of terms \( n \) is 50.
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Calculate the upper partial sum \( S_n \): The formula for the sum of the first \( n \) terms of an arithmetic sequence is given by: \[ S_n = \frac{n}{2} \times (a_1 + a_n) \] Where \( a_n \) is the last term.
For \( n = 50 \): \[ S_{50} = \frac{50}{2} \times (a_1 + a_{50}) = 25 \times (68.7 + (-44)) \] Simplifying: \[ S_{50} = 25 \times (68.7 - 44) = 25 \times 24.7 = 617.5 \]
Thus, the upper partial sum \( S_{50} \) is \( 617.5 \).
\[ \boxed{617.5} \]