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Q.6 For an arithmetic progression if \( S_{p}=q, S_{q}=p ; p \neq q \) prove that \( S_{p+q}=-(p+q) \).

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Q.6 For an arithmetic progression if \( S_{p}=q, S_{q}=p ; p \neq q \) prove that \( S_{p+q}=-(p+q) \).
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1 Answer

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Formula,

\(S_n =\frac{n}{2}[2a + (n-1)d]\)

Consider sum of first p terms,

Consider sum of first q terms,

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