• Q. Insert 12 numbers between 39 and 69 such that the resulting sequence is an A.P.
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  • Solve:-
    Let A1, A2, A3, A4,.... and A12 be 12 numbers between 39 and 69 such that

    39, A1, A2, A3, A4,....A12, 69 are in A.P.

    Here, a = 39, b = 69, n = 14,

    Therefore, 69 = 39 + (14 –1)d

    => 30 = 13 d

    so that d = 2.3076923076923

  • Thus,
    A1, A2, A3, A4, ......... A12

    = (39+2.3076923076923), (39+2*2.3076923076923), (39+3*2.3076923076923), (39+ 4*2.3076923076923), ...., (39+12*2.3076923076923)

    = 41.307692307692, 43.615384615385, 45.923076923077, 48.230769230769, ...., 66.692307692308

    Hence, 12 numbers between 39 and 69 are 41.307692307692, 43.615384615385, 45.923076923077, 48.230769230769, .... and 66.692307692308

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