To find the 12th term (\(a_{12}\)) of the arithmetic sequence given by -17, -13, -9, ..., we first need to determine the first term and the common difference.
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Identify the first term (\(a_1\)): \[ a_1 = -17 \]
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Determine the common difference (\(d\)): \[ d = a_2 - a_1 = -13 - (-17) = -13 + 17 = 4 \]
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Use the formula for the \(n\)-th term of an arithmetic sequence: \[ a_n = a_1 + (n - 1)d \]
Plugging in \(n = 12\): \[ a_{12} = a_1 + (12 - 1) \cdot d \] \[ a_{12} = -17 + 11 \cdot 4 \] \[ a_{12} = -17 + 44 \] \[ a_{12} = 27 \]
Thus, the 12th term (\(a_{12}\)) of the sequence is 27.