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KCET2014MathematicsProbability

Consider an infinite geometric series with first term ' ( a ) ' and common ratio ' ( r ) '. If the sum is ( 4 ) and the second term is ( 3 4 ), then

Options

  1. A( a= 4 7 , r= 3 7 )
  2. B( a=3, r= 1 4 )
  3. C( a=2, r= 3 8 )
  4. D( a= 3 2 , r= 1 2 )

Correct answer

B. ( a=3, r= 1 4 )

Step-by-step solution

Given that, first term is a and common ratio is ( r ). and ( t₂= 3 4 ) ( a r= 3 4 (1) ) Now, ( 4= a 1-r a=4-4 r ) ( 4 r=4-a (2) ) From Eqs. (1) and (2), we get ( a=3, r= 1 4 )

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