A carbon sequestration plant is gradually scaling up its operations. On the first day of its new cycle, the plant captures 18 tonnes of carbon dioxide. Each subsequent day, the amount of carbon dioxide captured increases by 2.5 tonnes.
Determine an expression for the amount of carbon dioxide captured on the n n\,nth day of the cycle.
The plant has a daily operational target of at least 150.5 tonnes. Calculate the number of days required to reach this specific target for the first time.
An environmental analyst predicts that by the time the plant hits this target, the total amount of carbon dioxide sequestered during the cycle will exceed 4,500 tonnes. Determine, with a calculation, whether the analyst's prediction is correct.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.