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Calculate the sum of the first \$$\\var{n}\$$ terms of this series.

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\$$S_\\var{n}=\$$ [[0]]

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If the difference between successive pairs of terms is a constant then the series under examination is an arithmetic progression.

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Ths first term is \$$a\$$ and the common difference is \$$d\$$.

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The formula for the nth term of the series is given by:    \$$S_n=\\frac{n}{2}\\left(2a+(n-1)d\\right)\$$

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In this example \$$a=\\var{a}\$$,  \$$d = \\var{d}\$$  and  \$$n = \\var{n}\$$

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\$$S_\\var{n}=\\frac{\\var{n}}{2}\\left(2*\\var{a}+(\\var{n}-1)\\var{d}\\right)\$$

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\$$S_\\var{n}=\\simplify{{n}/{2}}\\left(\\simplify{2{a}}+\\simplify{({n}-1)*{d}}\\right)\$$

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\$$S_\\var{n}=\\simplify{{n}/{2}}\\left(\\simplify{2{a}+({n}-1)*{d}}\\right)\$$

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\$$S_\\var{n}=\\simplify{{n}*{a}+{n}*({n}-1)*{d}/2}\$$

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\$$\\var{a} + \\simplify{{a}+{d}} + \\simplify{{a}+2*{d}}\\,+ \\, ...........\$$