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If a,b,c are in A.P. Prove …

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If a,b,c are in A.P. Prove that b+c,c+a,a+b are also in A.P.?

    • Posted by Khushi Chauhan 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    b + c, c + a, a + b will be in AP, if
    (c + a) - (b + c) = (a + b) - (c + a)
    {tex}\Rightarrow{/tex} a - b = b - c {tex}\Rightarrow{/tex} 2b = a + c
    i.e., a, b, c are in AP.
    Thus, a, b, c are in AP implies b + c, c + a, a + b are also in AP.
    Hence proved.

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