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To find the general term \( a_n \) of the arithmetic sequence, we use the formula for the \(n\)-th term of an arithmetic sequence:

\[
a_n = a_1 + (n-1) \cdot d
\]

where:
- \(a_1\) is the first term,
- \(d\) is the common difference, and
- \(n\) is the term number.

From the problem, we know:
- \(a_1 = 59\) (seats in the first row),
- \(a_2 = 64\) (seats in the second row),
- \(a_3 = 69\) (seats in the third row).

To find the common difference \(d\), we calculate:

\[
d = a_2 - a_1 = 64 - 59 = 5
\]

Thus, the common difference \(d = 5\).

Now, substituting into the general term formula:

\[
a_n = 59 + (n-1) \cdot 5
\]
\[
a_n = 59 + 5n - 5
\]
\[
a_n = 5n + 54
\]

So, the general term \(a_n\) for the sequence is:

\[
a_n = 5n + 54
\]

### Number of Seats in the 20th Row:
To find the number of seats in the 20th row, substitute \(n = 20\) into the formula for \(a_n\):

\[
a_{20} = 5(20) + 54 = 100 + 54 = 154
\]

Thus, there are **154 seats** in the 20th row.

Would you like further details or have any questions? Here are five related questions for you:

1. What is the formula for the sum of the first \(n\) terms of an arithmetic sequence?
2. How would the formula change if the common difference were negative?
3. How do you find the common difference when more terms are provided?
4. Can arithmetic sequences have fractional common differences?
5. What is the relationship between arithmetic sequences and linear equations?

**Tip:** In arithmetic sequences, the difference between consecutive terms is always constant, making the sequence linear.

An auditorium has 59 seats in the first row, 64 seats in the second row, 69 seats in the third row, and so on. Find the general term of this arithmetic sequence and the number of seats in the twentieth row.

Explore how to determine the number of seats in each row of an auditorium using the concept of arithmetic sequences. This problem involves calculating the general term and the seats in the 20th row, with clear applications in organizing seating arrangements.

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