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If the difference between successive pairs of terms is a constant then the series under examination is an arithmetic progression.
\nThs first term is \\(a\\) and the common difference is \\(d\\).
\nThe formula for the nth term of the series is given by: \\(S_n=\\frac{n}{2}\\left(2a+(n-1)d\\right)\\)
\nIn this example \\(a=\\var{a}\\), \\(d = \\var{d}\\) and \\(n = \\var{n}\\)
\n\\(S_\\var{n}=\\frac{\\var{n}}{2}\\left(2*\\var{a}+(\\var{n}-1)\\var{d}\\right)\\)
\n\\(S_\\var{n}=\\simplify{{n}/{2}}\\left(\\simplify{2{a}}+\\simplify{({n}-1)*{d}}\\right)\\)
\n\\(S_\\var{n}=\\simplify{{n}/{2}}\\left(\\simplify{2{a}+({n}-1)*{d}}\\right)\\)
\n\\(S_\\var{n}=\\simplify{{n}*{a}+{n}*({n}-1)*{d}/2}\\)
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\n\\(\\var{a} + \\simplify{{a}+{d}} + \\simplify{{a}+2*{d}}\\,+ \\, ...........\\)
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\n\\(S_\\var{n}=\\) [[0]]
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", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "name": "Arithmetic progression: The sum of the first n terms of a series", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}