A contractor stacks bricks in square‐based piles. The first pile contains 12 bricks, the second pile 22 bricks, the third pile 32 bricks, and so on. Each brick has a mass of 2kg.
(i) Derive an expression, in terms of n, for the total number of bricks in the first n piles.
(ii) Using your expression from part (i), find the total mass of bricks, in kilograms, in the first 20 piles.
(iii) If the contractor plans to build up to 50 piles, calculate the additional mass of bricks required to extend the stack from 20 piles to 50 piles.