An industrial filtration system is used to remove heavy metals from wastewater. The mass of metals removed during the n n\,nth hour of operation is given by un u_n\,un mg, where u1,u2,u3,… u_1, u_2, u_3, \dots\,u1,u2,u3,… forms a geometric series. The maximum possible total mass of metals the system can ever remove is 192 mg.
In the second hour of operation, the system removes 45 mg.
The mass removed in the first hour, aaa, is greater than 100 mg.
Find the first term, aaa, and the common ratio, rrr, of the series.
Show that the mass removed in the n n\,nth hour can be written as
un=3n⋅523n−6 u_n = \frac{3^n \cdot 5}{2^{3n-6}} un=23n−63n⋅5Hence show that
log2un=n(log23−3)+(6+log25) \log_2 u_n = n(\log_2 3 - 3) + (6 + \log_2 5) log2un=n(log23−3)+(6+log25)Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
