To find the coefficient of the second term in the expansion of \((a + 3)^7\), we can use the binomial theorem, which states:
\[ (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \]
In this case, \(a = a\), \(b = 3\), and \(n = 7\). The \(k\)-th term in the expansion is given by:
\[ \binom{n}{k} a^{n-k} b^k \]
Specifically, we're interested in the second term, which corresponds to \(k=1\).
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Calculate the binomial coefficient \(\binom{7}{1}\): \[ \binom{7}{1} = 7 \]
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Calculate \(a^{7-1} = a^6\).
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Calculate \(b^1 = 3^1 = 3\).
Putting this together, the second term is:
\[ \binom{7}{1} a^{6} \cdot 3^1 = 7 \cdot a^{6} \cdot 3 = 21a^6 \]
Thus, the coefficient of the second term in the expansion is \(21\).
Therefore, the answer is:
21.