Maths-
General
Easy

Question

In a geometric progression (GP) the ratio of the sum of the first three terms and first six terms is 125:152 the common ratio is

  1. fraction numerator 1 over denominator 5 end fraction    
  2. fraction numerator 2 over denominator 5 end fraction    
  3. fraction numerator 4 over denominator 5 end fraction    
  4. fraction numerator 3 over denominator 5 end fraction    

The correct answer is: fraction numerator 3 over denominator 5 end fraction


    Since, fraction numerator a plus a r plus a r to the power of 2 end exponent over denominator a plus a r plus a r to the power of 2 end exponent plus a r to the power of 3 end exponent plus a r to the power of 4 end exponent plus a r to the power of 5 end exponent end fraction equals fraction numerator 125 over denominator 162 end fraction
    rightwards double arrow fraction numerator 1 plus r plus r to the power of 2 end exponent over denominator open parentheses 1 plus r plus r to the power of 2 end exponent close parentheses open parentheses 1 plus r to the power of 3 end exponent close parentheses end fraction equals fraction numerator 125 over denominator 162 end fraction
    rightwards double arrow 1 plus r to the power of 3 end exponent equals fraction numerator 152 over denominator 125 end fraction
    rightwards double arrow r to the power of 3 end exponent equals fraction numerator 27 over denominator 125 end fraction equals open parentheses fraction numerator 3 over denominator 5 end fraction close parentheses to the power of 3 end exponent
    rightwards double arrow blank r equals fraction numerator 3 over denominator 5 end fraction

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