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Rajan@2021
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The sum of first 10 terms of an AP is -150 and the sum of its next 10 terms is -550. Find the AP.

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An important question from arithmetic progression chapter as it was already asked in previous year paper of 2010 in which we have been asked to find the AP if the sum of first 10 terms of an AP is -150 and the sum of its next 10 terms is -550.

RS Aggarwal, Class 10, chapter 5C, question no 31.

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1 Answer

  1. Given,

    S10=150
    S20S10= Next 10 term
    S20S10=550
    S20=550+S10
    S20=550150
    S20=700
    Sn=n/2[2a+(n1)d]

    S10=10/2[2a+(101)d]=150

    2a+9d=30       (i)

    S20=700

    20/2[2a+19d]=700

    2a+19d=70     (ii)

    eq(i)-eq(ii)

    (2a+9d=−30)(2a+19d=−70)
    10d=40
    d=4

    2a+9d=30
    2a=30+36
    a=3

    So the A.P. will be as:-
    a, (a+d), (a+2d), …

    3, (-1), (-5) & so on

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