To find the first three terms of the sequence defined by the nth term \( a_n = 3 \cdot 2^{n-2} \), we will substitute \( n = 1 \), \( n = 2 \), and \( n = 3 \) into the equation.
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For \( n = 1 \): \[ a_1 = 3 \cdot 2^{1-2} = 3 \cdot 2^{-1} = 3 \cdot \frac{1}{2} = \frac{3}{2} \]
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For \( n = 2 \): \[ a_2 = 3 \cdot 2^{2-2} = 3 \cdot 2^{0} = 3 \cdot 1 = 3 \]
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For \( n = 3 \): \[ a_3 = 3 \cdot 2^{3-2} = 3 \cdot 2^{1} = 3 \cdot 2 = 6 \]
Thus, the first three terms of the sequence are: \[ \frac{3}{2}, , 3, , 6 \]