Lemmara logoLemmaraWorked solution

WMA12/01 Oct 2023, Question 8: Arithmetic Progressions in Problems

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Theatre seating: first row has a seats, each later row 4 more, first 10 rows total 360. Find a, then use a total of 2146 seats over n rows to form and solve an equation and find the largest row.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Find the value of a given the first 10 rows contain 360 seats.

  1. 1S₁₀ = (10/2)(2a + 9 × 4) = 360
  2. 25(2a + 36) = 360, so 2a + 36 = 72
  3. 3a = 18

Answera = 18

Part (b) · 2 marks

Using the total of 2146 seats in n rows, show that n² + 8n − 1073 = 0.

  1. 1Sₙ = (n/2){2 × 18 + (n − 1) × 4} = 2146
  2. 2(n/2)(4n + 32) = 2146, so n(2n + 16) = 2146
  3. 32n² + 16n − 2146 = 0
  4. 4Divide by 2: n² + 8n − 1073 = 0

AnswerShown: (n/2){36 + 4(n − 1)} = 2146 ⇒ n(16 + 2n) = 2146 ⇒ n² + 8n − 1073 = 0

Part (ci) · 1 mark

State how many rows of seats the theatre has.

  1. 1n² + 8n − 1073 = (n − 29)(n + 37) = 0
  2. 2n = 29 (n = −37 is impossible)

Answer29 rows

Part (cii) · 2 marks

Find the greatest number of seats in any single row.

  1. 1The last row has the most seats: a + (n − 1) × 4
  2. 2= 18 + 28 × 4 = 130

Answer130 seats

Stuck on a step? Read the free lesson: Arithmetic Progressions in Problems

Practise more arithmetic progressions in problems questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on arithmetic progressions in problems

Also searched as: WMA12 October 2023 · WMA12/01 · wma12 oct23 · IAS Maths Pure Mathematics 2 October 2023 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.