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In an AP the first term …

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In an AP the first term is 2 and the sum of the first five terms is one fourth of the sum of the next five terms . Show that the 20th term is -112

    • Posted by Raj Goswami 6 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 6 years, 9 months ago

     a=2,sum of first five terms =1/4th sum of next five terms

    this gives,, 4 times of sum of first five terms =sum of next five terms

    sum of first five terms + sum of next five terms = to sum of first ten terms

    sum of first five terms + 4 times of sum of first five terms=sum of first ten terms

    5 times of sum of first five terms =sum of first ten terms

    5*n/2[2a+4d]=n/2[2a+9d]             :(a=2}

    5*5/2[4+4d]=10/2[4+9d]

    25/2[4+4d]=5[4+9d]

    5[4+4d]=2[4+9d]

    20+20d=8+18d

    so,d=  -6

     

    a20 = a+ 19d

    = 2 + 19(-6)

    = 2 - 114

    = -112

    2Thank You

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