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if x , 2y and 3z are in AP where the distinct numbers x, yand z are in gp. Then the common ratio of the GP isA. 3B. `(1)/(3)`C. 2D. `(1)/(2)` |
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Answer» Correct Answer - B Given x, 2y and 3z are in AP , then ,`2y=(x+3z)/(2)` `implies y=(x+3z)/(4)` `implies 4y=x+3z` and x,y,z are in GP then `(y)/(x)=(z)/(y) =lamda` `implies y=x lamda and z=lamday - lamda^(2)x` On subsitiuting these values in Eq (i) we get `4(x, lamda )=x+3(lamda^(2)x)` `implies 4lamdax=x+3lamda^(2)x` `implies 4lamda=1+3lamda^(2)` `implies 3lamda ^(2) -4lamda+1=0` `=(3lamda-10(lamda-1)=0` `therefore lamda =(1)/(3).lamda =1 ` |
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