Transum Software

Exam-Style Question on Sequences

A mathematics exam-style question with a worked solution that can be revealed gradually

List Of Questions Exam-Style Question More Sequences Questions More on this Topic

Question id: 20. This question is similar to one that appeared on an IB Studies paper in 2012. The use of a calculator is allowed.

A Grecian amphitheatre was built in the form of a horseshoe and has 22 rows.

The number of seats in each row increase by a fixed amount, \(d\), compared to the number of seats in the previous row. The number of seats in the fifth row, \(u_5\), is 58, and the number of seats in the ninth row, \(u_{9}\), is 86. \(u_1\) represents the number of seats in the first row.

(a) Write an equation for \(u_5\) in terms of \(d\) and \(u_1\).

(b) Write an equation for \(u_{9}\) in terms of \(d\) and \(u_1\).

(c) Write down the value of \(d\);

(d) Write down the value of \(u_1\).

(e) Find the total number of seats in the amphitheatre.

Some time later, a second level was added to increase the amphitheatre’s capacity by another 2590 seats. Each row has five more seats than the previous row. The first row on this level has 82 seats.

(f) Find the number of rows on the second level of the amphitheatre.

The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.

Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.

This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.

A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.



Drag this panel down to reveal the solution

If you need more practice try the self-checking interactive exercise called Sequences and Series.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.


Exam-Style Questions Main Page


Search for exam-style questions containing a particular word or phrase:

To search the entire Transum website use the search box in the grey area below.


Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2023 WWW.TRANSUM.ORG

©1997 - 2023 Transum Mathematics :: For more exam-style questions and worked solutions go to