If a, b, c are in A.P.,then 10^{ax + 10}, 10^ | vedclass

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(C) Given that $a, b, c$ are in $A.P.$$ \Rightarrow 2b = a + c $Consider the terms $10^{ax + 10}, 10^{bx + 10}, 10^{cx + 10}$.For these terms to be in

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$G.P.$ for all values of $x$

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(C) Given that $a, b, c$ are in $A.P.$$ \Rightarrow 2b = a + c $Consider the terms $10^{ax + 10}, 10^{bx + 10}, 10^{cx + 10}$.For these terms to be in $G.P.$,the square of the middle term must equal the product of the first and third terms:$(10^{bx + 10})^2 = 10^{2(bx + 10)} = 10^{2bx + 20}$Product of first and third terms: $10^{ax + 10} 	imes 10^{cx + 10} = 10^{ax + cx + 20} = 10^{(a+c)x + 20}$Since $a + c = 2b$,we have $10^{(a+c)x + 20} = 10^{2bx + 20}$.Thus,$(10^{bx + 10})^2 = 10^{ax + 10} 	imes 10^{cx + 10}$ holds true for all values of $x$.Therefore,the terms are in $G.P.$ for all values of $x$.

If $a, b, c$ are in $A.P.$,then $10^{ax + 10}, 10^{bx + 10}, 10^{cx + 10}$ will be in

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