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AP EAMCET202423 May 2024Morning ShiftMathematicsSequences and SeriesActual

The number of ways of selecting 3 numbers that are in G.P. from the set 1,2,3, , 100 is

Options

  1. A18
  2. B52
  3. C14
  4. D53

Correct answer

D. 53

Step-by-step solution

Let three numbers in G.P. be a , a r, a r^2 , such that a r^2 100 a 100 r^2 and a be a positive integer. So, a= [ 100 r^2 ], 2 r 10 aligned &= [ 100 4 ]+ [ 100 9 ]+ [ 100 16 ]+ [ 100 25 ]+ [ 100 36 ] &+ [ 100 49 ]+ [ 100 64 ]+ [ 100 81 ]+ [ 100 100 ] aligned =25+11+6+4+2+2+1+1+1=53 .

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