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.
178 exam-style questions on Edexcel A Level Maths Sequences and Series, 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. Each one has a worked solution and a mark scheme showing where the marks go.