- The problem requires calculating the total number of seats in a cinema hall based on its seating arrangement.
- The hall has 10 rows of seats.
- The first row has 25 seats.
- Each subsequent row has 3 more seats than the previous row, forming an arithmetic sequence.
- The number of seats in the nth row is given by the formula: $a_n = a_1 + (n-1)d$, where $a_1 = 25$ and $d = 3$.
- The total number of seats is the sum of the first 10 terms of this arithmetic sequence.
- The sum of the first n terms of an arithmetic sequence is calculated using the formula: $S_n = \frac{n}{2} \times (2a_1 + (n-1)d)$.
- Substituting the values: $S_{10} = \frac{10}{2} \times (2 \times 25 + (10-1) \times 3)$.
- This simplifies to: $S_{10} = 5 \times (50 + 27) = 5 \times 77 = 385$.
- Therefore, the total number of seats in the cinema hall is 385.
Parent Tip: Review the logic above to help your child master the concept of blank unit circle worksheet.
