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Rajan@2021
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Find the sum of the following arithmetic series: 7 + 10 1/2 + 14 +….+ 84.

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A basic and conceptual question from arithmetic progression chapter in which we are to find the sum of the given arithmetic series

7 + 10 1/2 + 14 +….+ 84.

RS Aggarwal, Class 10, chapter 5C, question no 2(i).

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1 Answer

  1. In given series of AP first term a=7, common difference d= 1021​−7=221​−7=27​ and last term l=84
    Since, l=a+(n−1)d
    ⇒84=7+(n−1)27​
    ⇒84−7=(n−1)27​
    ⇒77=(n−1)27​
    ⇒77×72​=n−1
    ⇒22=n−1
    ⇒n=23
    Since, Sn​=n​/2(a+l)
    ⇒Sn​=23/2​(7+84)
    ⇒Sn​=91×23/2​
    ⇒Sn​=2093/2​
    ⇒Sn​=1046 1/2​

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