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.
308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.