To find the first three terms of the sequence defined by \( a_n = 4^n \), we will calculate the values of \( a_1 \), \( a_2 \), and \( a_3 \):
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For \( n = 1 \): \[ a_1 = 4^1 = 4 \]
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For \( n = 2 \): \[ a_2 = 4^2 = 16 \]
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For \( n = 3 \): \[ a_3 = 4^3 = 64 \]
Thus, the first three terms of the sequence are:
\[ \boxed{4, 16, 64} \]