A deep-sea research station, Project Alpha, is extracting mineral core samples from the seabed. In the first month of operation, the station extracts 150 kg of minerals. As the crew becomes more efficient, the mass extracted increases by 5 kg each subsequent month, such that they extract 155 kg in the second month, 160 kg in the third month, and so on, forming an arithmetic sequence.
Find the mass of minerals extracted by Project Alpha in the 20th month. (2)
Find the total mass of minerals extracted by Project Alpha over the first 50 months of operation. (3)
A secondary robotic drill, Project Beta, is also extracting minerals.
Project Beta extracts 695 kg in the first month, but due to mechanical wear, the mass extracted decreases by 10 kg each subsequent month, so that it extracts 685 kg in the second month, 675 kg in the third month, and so on, forming an arithmetic sequence.
Project Beta is decommissioned as soon as the total mass of minerals it has extracted reaches exactly 20,000 kg.
Given that Project Beta reaches this total after n n\,n months, form an equation in n n\,n and show that it can be simplified to
n2−140n+4000=0 n^2 - 140n + 4000 = 0 n2−140n+4000=0(3)
Solve the equation in part (c). (2)
State, with a reason, which of the solutions to the equation in part (c) is not a sensible value for n n\,n in this context. (1)
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.