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If the third term of an ap is 1 and 6th term is -11find the sum of its first 32term

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An important question from ML Aggarwal  It is given that the third term of an ap is 1 and 6th term is -11, find the sum of its first 32term.

Arithmetic Progression Chapter 9 Question no 10

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  1. Given,

    a3=1
    a6=11

    nth term of A.P. is calculated as,
    an=a1+(n1)d

    For 3rd term, put n=3
    a3=a1+(31)d
    1=a1+(2)d
    a1+2d=1          Equation (1)

    For 6th term, put n=6
    a6=a1+(61)d
    11=a1+(5)d
    a1+5d=11         Equation (2)

    Subtract equation (1) from (2), we get,

    (a1a1)+(5d2d)=111
    3d=12
    d=4

    Put this value in equation (1), we get,
    a1+2(4)=1
    a18=1
    a1=9

    Thus, sum of first 32 terms is calculated by,
    an=2n[2a+(n1)d]

    an=232[(2×9)+(321)(4)]

    an=16[18+31(4)]

    an=16[18124]

    an=16[106]

    an=1696

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