In this question you must show detailed reasoning.
A chemical reactor is being commissioned over a 12-day period. During this period, a technician performs a primary catalyst injection every morning and a secondary maintenance flush every afternoon.
The technician considers two different commissioning protocols for the morning injections.
In Protocol A, the volume of catalyst injected each morning increases by the same constant amount each day.
Calculate the volume of catalyst injected on the morning of day 8 under Protocol A. (3)
In Protocol B, the volume of catalyst injected each morning increases by a constant percentage each day.
Calculate the volume of catalyst injected on the morning of day 8 under Protocol B. Give your answer in liters to one decimal place. (3)
Additionally, a fixed volume, vvv liters, is used for the maintenance flush every afternoon for the entire 12-day period. Given that:
(i) Determine the maximum possible value of vvv if Protocol A is used. (ii) Determine the maximum possible value of vvv if Protocol B is used. (5)
178 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.