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 Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 156 questions covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series, matched to the Edexcel A Level Maths (9MA0) 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.
