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Rajan@2021
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The sum of first 9 terms of an AP is 81 and that of its first 20 terms is 400. Find the first term and the common difference of the AP.

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I have a question from arithmetic progression chapter in which we are to find the first term and the common difference of an AP, if the sum of first 9 terms of an AP is 81 and that of its first 20 terms is 400.

Book – RS Aggarwal, Class 10, Chapter 5C, question no 28

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  1. Sum of the term Sn​=n/2​[2×a+(n−1)d]
    Given sum of 9 terms =81
    81=9/2​[2a+(9−1)d]...(1)
    Sum of 20 terms =400
    400=20​/2[2a+(20−1)d]...(2)
    ⇒81=9​/2[2a+8d]
    ⇒400=29​[2a+19d]
    ⇒162=18a+72d...(3)
    ⇒400=20a+190d....(4)
    Multiply eq(3) by 20 and and eq(4) by 18 and subtract both the equation
    ⇒360a+3420d=7200
    ⇒360a+1440d=3240
    1980d=3690
    ⇒d=2
    Now substitute the d=2 in eq(4)
    ⇒400=20a+190×2
    ⇒400=20a+380
    ⇒20a=20
    ⇒a=1

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