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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}\\)
\n", "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "The first three terms of a series are given by:
\n\\(\\var{a} + \\simplify{{a}+{d}} + \\simplify{{a}+2*{d}}\\,+ \\, ...........\\)
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\n\\(S_\\var{n}=\\) [[0]]
"}], "type": "question", "contributors": [{"name": "Andrew Dunbar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/770/"}]}]}], "contributors": [{"name": "Andrew Dunbar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/770/"}]}