Let Sn be the sum of the first n terms of the arithmetic series 2 + 4 + 6 + ... i) Find S4

Firstly look for key terms in the question, identifying that we are going to be finding the sum of n terms, and it is an arithmetic series. This allows us to know which equations to look for in our formula booklet, the following equations are relevant: S_n = (n/2)(2u₁ + d(n-1)) = n/2(u₁ + u_n) u_n = u₁ + d(n-1) There are two ways of solving this problem, but first it is done by identifying the first term and the difference between the terms. In this case u₁ = 2, because it is the first term, and the difference between 2 and 4 is 2, which is the same difference between 4 and 6 which means that d = 2. Since we are trying to find the sum of all terms up to the 4th term then n=4. If we put these defined terms into the equation then we can derive the answer. S_n = (n/2)(2u₁ + d(n-1))   S₄ = (4/2) (2 x 2 + 2(4-1))  S₄ = 2 (4 + (2 x 3)) S₄ = 20