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KCET2015MathematicsStraight Lines

If the ( 2^ nd ) and ( 5^ th ) terms of G.P. are ( 24 ) and ( 3 ) respectively, then the sum of ( 1^ st ) six terms is

Options

  1. A( 189 2 )
  2. B( 189 5 )
  3. C( 179 2 )
  4. D( 2 189 )

Correct answer

A. ( 189 2 )

Step-by-step solution

Given that, T₂=24 and T₅=3 Now, a r=24 (1) and a r⁴=3 (2) Dividing Eq. (2) by Eq. (1), we have a r⁴ a r = 3 24 r³= 1 8 r= 1 2 So, from Eq. (1), we have a=24 2=48 Therefore, S₆= a (1-r⁵ ) 1-r = 48 (1-(1 / 2)⁶ ) 1-1 / 2 = 189 2

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