If (k – 2, (2k +1), (6 k + 3) are in GP, then k = ?

  1. 2
  2. 7
  3. 3
  4. 6
Anurag Mishra Professor Asked on 18th April 2016 in Maths.
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  • 1 Answer(s)

    Answer: (2) 7 

    Solution:-
    (k – 2), (2k + 1), (6k + 3)

    Formula-
    b2 = ac , a = first term, b = second term and c = third term.

    Then,
    (2 k + 1)2 =  (k – 2) (6 k + 3)
    4 k2 +  1 + 2 x 2 k x 1 = 6k x k + 3 k – 12 k – 6
    4 k2 + 4 k + 1 = 6 k2  – 9 k  – 6
    2 k2  – 13 k – 7 = 0

    2 k2  –  14 k  + k – 7 = 0
    2 k ( k – 7) + 1 (k – 7) = 0
    (2 k + 1) (k – 7) = 0
    k – 7 = 0
    k = 7

    Then, the value of k is 7.

    Hence, the correct answer is option (2) 7.

    Anurag Mishra Professor Answered on 23rd April 2016.
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