How to deduce the sum of split terms of arithmetic sequence?

The tolerance of {an} arithmetic sequence is d
Sn＝a1＋(a1＋d)＋(a1＋2d)＋… ＋[a1＋(n－1)d],
Sn＝an＋(an－d)＋(an－2d)＋… ＋[an－(n－1)d],
The sum of the two formulas gives 2Sn = n (a1 + an) ∧ Sn = n (a1 + an) / 2

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