1. **State the problem:** We have a linear sequence where the first term $a_1 = 9$ and the common difference $d = 7$. We want to find the value of $n$ when the $n$th term $a_n = 380$. 2. **Formula for the $n$th term of an arithmetic sequence:** $$a_n = a_1 + (n-1)d$$ This formula tells us how to find any term in the sequence based on its position $n$. 3. **Substitute the known values:** $$380 = 9 + (n-1)7$$ 4. **Simplify the equation:** $$380 = 9 + 7n - 7$$ $$380 = 7n + 2$$ 5. **Isolate $n$:** $$380 - 2 = 7n$$ $$378 = 7n$$ 6. **Divide both sides by 7:** $$\cancel{7}n = \frac{378}{\cancel{7}}$$ $$n = 54$$ 7. **Answer:** The value of $n$ is 54, which corresponds to option B.