Question: Use the rule to complete the table.
5. The first row of the movie theater has $10$ seats. Each row has $4$ additional seats than the previous row. How many seats are in the rows shown in the table?
Row $4$: $4 \times 4 + 10 = 26$
Row $5$: $5 \times 4 + 10 = 30$
Row $6$: $6 \times 4 + 10 = 34$
1. **State the problem:** We need to find the number of seats in each row of a movie theater where the first row has $10$ seats and each subsequent row has $4$ more seats than the previous one.
2. **Formula used:** The number of seats in row $n$ can be expressed as:
$$\text{Seats in row } n = 10 + 4(n - 1)$$
This is because the first row has $10$ seats, and each next row adds $4$ seats.
3. **Check given rows:**
- For row $4$:
$$10 + 4(4 - 1) = 10 + 4 \times 3 = 10 + 12 = 22$$
But the user used $4 \times 4 + 10 = 26$, which is a different formula.
4. **Analyze the user's formula:**
User's formula is:
$$\text{Seats} = 4n + 10$$
Check for $n=4$:
$$4 \times 4 + 10 = 16 + 10 = 26$$
This matches the user's calculation.
5. **Explain the difference:**
The user's formula assumes the first row has $14$ seats (since for $n=1$, seats = $4 \times 1 + 10 = 14$), which contradicts the problem statement.
6. **Correct formula:**
Since the first row has $10$ seats, and each row adds $4$ seats, the correct formula is:
$$\text{Seats} = 10 + 4(n - 1)$$
7. **Calculate seats for rows 4, 5, and 6:**
- Row $4$:
$$10 + 4(4 - 1) = 10 + 12 = 22$$
- Row $5$:
$$10 + 4(5 - 1) = 10 + 16 = 26$$
- Row $6$:
$$10 + 4(6 - 1) = 10 + 20 = 30$$
8. **Summary:**
| Row | Seats (correct) |
|-----|-----------------|
| 4 | 22 |
| 5 | 26 |
| 6 | 30 |
The user's formula overestimates the seats by $4$ for each row.
**Final answer:**
Row $4$ has $22$ seats.
Row $5$ has $26$ seats.
Row $6$ has $30$ seats.