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KCET2026MathematicsSequences and Series

If we insert two numbers between 2 and 4 so that the resulting sequence is in G.P, then the inserted numbers in the order are

Options

  1. A8, 2
  2. B2, 8
  3. C8 , 2
  4. D2 , 8

Correct answer

B. 2, 8

Step-by-step solution

Let the geometric progression be a, ar, ar^2, ar^3 . Given a = 2 and ar^3 = 4 . Substituting the value of a , we get: 2 r^3 = 4 r^3 = 4 2 = 2 2 = ( 2 )^3 r = 2 The two inserted numbers are ar and ar^2 . ar = 2 2 = 2 ar^2 = 2 ( 2 )^2 = 2 2 = 8 The inserted numbers in order are 2 and 8 . Answer: 2, 8

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