If the 4^{th}, 7^{th} and 10^{th} terms of a | vedclass

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(C) Let the first term of the $G.P.$ be $A$ and the common ratio be $r$.We know that the $n^{th}$ term of a $G.P.$ is given by $T_n = A r^{n-1}$.Given

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$b^2 = ac$

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(C) Let the first term of the $G.P.$ be $A$ and the common ratio be $r$.We know that the $n^{th}$ term of a $G.P.$ is given by $T_n = A r^{n-1}$.Given terms are:$T_4 = a = A r^3$$T_7 = b = A r^6$$T_{10} = c = A r^9$Now,consider the product $ac$:$ac = (A r^3) 	imes (A r^9) = A^2 r^{12}$Also,consider $b^2$:$b^2 = (A r^6)^2 = A^2 r^{12}$Since $b^2 = A^2 r^{12}$ and $ac = A^2 r^{12}$,it follows that $b^2 = ac$.Therefore,$a, b, c$ are in $G.P.$

If the $4^{th}, 7^{th}$ and $10^{th}$ terms of a $G.P.$ are $a, b, c$ respectively,then the relation between $a, b, c$ is

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