- In a large theatre there are \(n\) rows of seats, where \(n\) is a constant.
The number of seats in the first row is \(a\), where \(a\) is a constant.
In each subsequent row there are 4 more seats than in the previous row so that
- in the 2 nd row there are \(( a + 4 )\) seats
- in the 3rd row there are ( \(a + 8\) ) seats
- the number of seats in each row form an arithmetic sequence
Given that the total number of seats in the first 10 rows is 360
- find the value of \(a\).
Given also that the total number of seats in the \(n\) rows is 2146
- show that
$$n ^ { 2 } + 8 n - 1073 = 0$$
- Hence
- state the number of rows of seats in the theatre,
- find the maximum number of seats in any one row.