OCR Pure 1 2017 Specimen — Question 7

Exam BoardOCR
ModulePure 1 (Pure Mathematics 1)
Year2017
SessionSpecimen
TopicGeometric Sequences and Series

7 Business A made a \(\pounds 5000\) profit during its first year.
In each subsequent year, the profit increased by \(\pounds 1500\) so that the profit was \(\pounds 6500\) during the second year, £8000 during the third year and so on. Business B made a \(\pounds 5000\) profit during its first year.
In each subsequent year, the profit was 90\% of the previous year's profit.
  1. Find an expression for the total profit made by business A during the first \(n\) years. Give your answer in its simplest form.
  2. Find an expression for the total profit made by business B during the first \(n\) years. Give your answer in its simplest form.
  3. Find how many years it will take for the total profit of business A to reach \(\pounds 385000\).
  4. Comment on the profits made by each business in the long term.