The first row of an open-air theatre has 20 seats and each succeeding row has 2 more…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
The first row of an open-air theatre has 20 seats and each succeeding row has 2 more seats than the previous one. The management wants to reserve a consecutive set of rows starting with the kth row and ending with the mth row (where m>k) such that:
(a) Part 1: (i) the total number of seats in these reserved rows is 420,
(b) Part 2: (ii) the last of the reserved rows has exactly 15 more seats than the first reserved row.
(c) Part 3: Find the values of k and m, and state the number of seats in each of the reserved rows.