A carbon sequestration facility is commissioned to remove carbon dioxide from the atmosphere. On the first day of operation, it captures 18.2518.2518.25 tonnes of CO2CO_2CO2. Each subsequent day, due to system calibration, the amount captured increases by exactly 1.251.251.25 tonnes over the previous day's total. The facility continues this process until a specific cumulative target is reached.
(i) State, with a reason, whether an arithmetic or a geometric series should be used to model the amount of CO2CO_2CO2 captured.
(ii) Write down an expression, in terms of nnn, for the mass, CnC_nCn, in tonnes, captured on day nnn.
Given that the facility's total sequestration target is 250025002500 tonnes, determine the number of days of operation required to reach this target.
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.