You should write arithmetic mean = (a1+a2+…+an) / n (use parenthesis to make your equation correct, this will also help you keep things straight)
What is (a1+a2+…+an )? it is ∑(ai) taken over i=1…n, no? The i subscript just serves as an index to your different data values, i=1 for the first one (a1), i=2 for the 2nd one (a2), etc., up to the nth one (an). The sigma notation ends up being more compact and easier to deal with in working out problems. Multiplying by (1/n) out in front just divides the sum by n, which is the arithmetic mean you started with at the beginning, so the two are equivalent.