A robotic printing head deposits layers of concrete to form a structural support pillar. The first layer has a thickness of 15.0 mm. Each subsequent layer is 2.5 mm thicker than the layer immediately preceding it. This process continues until the total height of the pillar reaches a specific requirement.
(i) State, with a reason, whether an arithmetic series or a geometric series should be used to model the thickness of the layers.
(ii) Determine an expression for the thickness of the nnn-th layer, TnT_nTn, in terms of nnn.
Given that the final height of the pillar must be at least 2100 mm, calculate the minimum number of layers required to complete the pillar.
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.
