If x, y, z are three positive numbers in G.P. | vedclass

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(D) Given that $x, y, z$ are in $G.P.$Taking the natural logarithm of each term,we get $\ln x, \ln y, \ln z$ in $A.P.$Let $a = \ln x, b = \ln y, c = \

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$A.G.P.$

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(D) Given that $x, y, z$ are in $G.P.$Taking the natural logarithm of each term,we get $\ln x, \ln y, \ln z$ in $A.P.$Let $a = \ln x, b = \ln y, c = \ln z$. Since they are in $A.P.$,we have $2b = a + c$.The given terms are $T_1 = \frac{1+a}{2}, T_2 = \frac{1+b}{4}, T_3 = \frac{1+c}{8}$.For these to be in $A.G.P.$,they must be of the form $ar^0, (a+d)r^1, (a+2d)r^2$. However,checking the ratio of differences or the structure,we observe that the terms follow the form of an Arithmetico-Geometric Progression where the linear part is in $A.P.$ and the denominator forms a $G.P.$Thus,the terms are in $A.G.P.$

If $x, y, z$ are three positive numbers in $G.P.$,then $\frac{1 + \ln x}{2}, \frac{1 + \ln y}{4}, \frac{1 + \ln z}{8}$ are in

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