If the coefficients of $x^7$ and $x^8$ in the expansion of $\left(2 + \frac{x}{3}\right)^n$ are equal, then $n$ equals:
Step-by-Step Solution
Key Concept: Write the general term $T_{r+1} = \binom{n}{r} 2^{n-r} \left(\frac{x}{3}\right)^r$, set the coefficients of $x^7$ and $x^8$ equal, and simplify the ratio $\frac{\binom{n}{7}}{\binom{n}{8}}$ using $\frac{\binom{n}{r}}{\binom{n}{r+1}} = \frac{r + 1}{n - r}$.
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Correct Answer: (1)