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Rajan@2021
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The sum of first 7 terms of an AP is 49 and the sum of its first 17 terms is 289. Find the sum of its first n terms.

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One of the most important and exam oriented question from arithmetic progression chapter in which we have been asked to find the sum of first n terms if the sum of first 7 terms of an AP is 49 and the sum of its first 17 terms is 289.

Book – RS Aggarwal, Class 10, chapter 5C, question no 29

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1 Answer

  1. By using Sn​=2n​[2a+(n−1)d] we have,

    S7​=7​/2[2a+(7−1)d]=49

    ⇒49=7​/2[2a+(7−1)d]

    ⇒49=7/2​(2a+6d)

    ⇒7=a+3d

    ⇒a+3d=7……………….(i)

    S17​=17/2​[2a+(17−1)d]=289

    ⇒289=17​/2[2a+(17−1)d]

    ⇒289=17/2​(2a+16d)

    ⇒17=a+8d

    ⇒a+8d=17………………….(ii)

    Substituting (i) from (ii), we get

    5d=10 or d=2

    From equation (i),

    a+3(2)=7

    a+6=7 or a=1

    Sn​=n/2​[2(1)+(n−1)2]

    =n/2​[2+(n−1)2]

    =n/2​(2+2n−2)
    =n^2

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