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\title{Deriving the summation formula of any Converged Arithmetic Series}
\author{Adrian D'Costa}
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\begin{align*}&S_{n} = (a + (n-1)d) + (a + (n-2)d) + (a + (n-3)d)... + (a + 2d )+ (a + d)\\& + a \\&S_{n} = a + (a + d) + (a + 2d ) + ... + (a + (n-3)d) + (a + (n-2)d)\\& + (a+ (n-1)d)\\&2S_{n} = 2na + [(n-1)d + d] + [(n-2)d + 2d] + ...+ [2d + (n-2)d]\\& + [d + (n-1)d]\\&2S_{n} = 2na + (n-1)nd\\&S_{n} = \frac{n}{2}[2a + (n-1)d]\\\text{or }S_{n} &= \frac{n}{2}[a + (a+ (n-1)d)]\\&=\frac{n}{2}(a+l)\text{ or } \frac{n}{2}(a_{0}+a_{n})\text{..........[Answer]}\end{align*}
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