- In a large theatre there are 20 rows of seats.
The number of seats in the first row is \(a\), where \(a\) is a constant.
In the second row the number of seats is \(( a + d )\), where \(d\) is a constant. In the third row the number of seats is \(( a + 2 d )\), and on each subsequent row there are \(d\) more seats than on the previous row. The number of seats in each row forms an arithmetic sequence.
The total number of seats in the first 10 rows is 395
- Use this information to show that \(10 a + 45 d = 395\)
The total number of seats in the first 18 rows is 927
- Use this information to write down a second simplified equation relating \(a\) and \(d\).
- Solve these equations to find the value of \(a\) and the value of \(d\).
- Find the number of seats in the 20th row of the theatre.