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Math

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In an A.P.the third term is 4 times the first term and the 6th term is 17. Find the series

  • Math - ,

    If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

    an = a1 + ( n - 1 ) * d


    a3 = a1 + ( 3 - 1 ) * d

    a3 = a1 + 2 d


    a3 = 4 a1

    4 a1 = a1 + 2 d

    4 a1 - a1 = 2d

    3 a1 = 2 d Divide both sides with 2

    3 a1 / 2 = d

    d = 3 a1 / 2


    an = a1 + ( n - 1 ) * d


    a6 = a1 + ( 6 - 1 ) * d = 17

    17 = a1 + 5 d

    17 = a1 + 5 * 3 a1 / 2

    17 = a1 + 15 a1 / 2

    17 = 2 a1 / 2 + 15 a1 / 2

    17 = 17 a1 / 2 Multiply both sides with 2

    34 = 17 a1 Divide both sides with 17

    34 / 17 = a1

    2 = a1

    a1 = 2


    d = 3 a1 / 2

    d = 3 * 2 / 2

    d = 6 / 2

    d = 3


    a1 = 2 , d = 3


    A.P.

    2 , 5 , 8 , 11 , 14 , 17 , 20 , 23 ...

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