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.
