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Question

Statement (I) : 27, 8 and 12 can be three terms of G.P. as well as an A.P
Statement (II) : Three non-zero real numbers can always be three terms of an A.P

  1. Statement-1 is True, Statement-2 is true; Statement-2 is a correct explanation for Statement-    
  2. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.    
  3. Statement-1 is True, Statement-2 is False.    
  4. Statement-1 is False, Statement-2 is True.    

The correct answer is: Statement-1 is True, Statement-2 is False.


    27 equals a r to the power of p minus 1 end exponent text  and  end text 12 equals a r to the power of s minus 1 end exponent
    fraction numerator 27 over denominator 8 end fraction equals r to the power of p minus q end exponent comma fraction numerator 8 over denominator 12 end fraction equals r to the power of q minus s end exponent
    table row cell therefore open parentheses fraction numerator 27 over denominator 8 end fraction close parentheses to the power of q minus s end exponent equals r to the power of left parenthesis p minus q right parenthesis comma left parenthesis q minus s right parenthesis end exponent text end text text a end text text n end text text d end text text end text open parentheses fraction numerator 8 over denominator 12 end fraction close parentheses to the power of left parenthesis p minus q right parenthesis end exponent equals r to the power of left parenthesis q minus s right parenthesis left parenthesis p minus q right parenthesis end exponent end cell row cell open parentheses fraction numerator 27 over denominator 8 end fraction close parentheses to the power of left parenthesis q minus s right parenthesis end exponent equals open parentheses fraction numerator 8 over denominator 12 end fraction close parentheses to the power of left parenthesis p minus q right parenthesis end exponent text end text text i end text text. end text text e end text text end text open parentheses fraction numerator 3 over denominator 2 end fraction close parentheses to the power of left parenthesis 3 q minus 3 s right parenthesis end exponent equals open parentheses fraction numerator 2 over denominator 3 end fraction close parentheses to the power of left parenthesis q minus s right parenthesis end exponent end cell end table
    3q –3s = q – p or 2q + p = 3s For any 3p, q, s >0, we get that 27, 8, 12 are three terms of G.P A is correct R is False

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