To find the sum of the first 9 terms of the arithmetic sequence \( a_n = 3n - 1 \), we first need to identify the first term \( a_1 \) and the ninth term \( a_9 \).
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Calculate the first term \( a_1 \): \[ a_1 = 3(1) - 1 = 2 \]
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Calculate the ninth term \( a_9 \): \[ a_9 = 3(9) - 1 = 27 - 1 = 26 \]
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Use the formula for the sum of the first \( n \) terms of an arithmetic sequence: The formula for the sum of the first \( n \) terms \( S_n \) of an arithmetic sequence is: \[ S_n = \frac{n}{2} \times (a_1 + a_n) \] where \( a_n \) is the nth term.
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Now substitute \( n = 9 \), \( a_1 = 2 \), and \( a_9 = 26 \): \[ S_9 = \frac{9}{2} \times (2 + 26) = \frac{9}{2} \times 28 \]
Thus, the equation that represents the sum of the first 9 terms is: \[ S_9 = \frac{9}{2} \times (2 + 26) \]
Therefore, the correct response is: \[ \text{upper } S_9 = \frac{9}{2} \left(2 + 26\right) \]