If frac{x + y}{2}, y, frac{y + z}{2} are in H | vedclass

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(B) Given that $\frac{x + y}{2}, y, \frac{y + z}{2}$ are in $H.P.$Since the terms are in $H.P.$,their reciprocals $\frac{2}{x + y}, \frac{1}{y}, \frac

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$G.P.$

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(B) Given that $\frac{x + y}{2}, y, \frac{y + z}{2}$ are in $H.P.$Since the terms are in $H.P.$,their reciprocals $\frac{2}{x + y}, \frac{1}{y}, \frac{2}{y + z}$ are in $A.P.$Therefore,$2 	imes \frac{1}{y} = \frac{2}{x + y} + \frac{2}{y + z}$$\frac{2}{y} = 2 \left( \frac{1}{x + y} + \frac{1}{y + z} ight)$$\frac{1}{y} = \frac{y + z + x + y}{(x + y)(y + z)}$$(x + y)(y + z) = y(x + 2y + z)$$xy + xz + y^2 + yz = xy + 2y^2 + yz$$xz = y^2$Since $y^2 = xz$,the terms $x, y, z$ are in $G.P.$

If $\frac{x + y}{2}, y, \frac{y + z}{2}$ are in $H.P.$,then $x, y, z$ are in

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