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

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Question

(c) Let first term of $G.P.$ $ = A$ and common ratio $ = r$

We know that ${n^{th}}$ term of $G.P. =$ $A{r^{n - 1}}$

Now ${t_4} = a = A{r^3},\;{t

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${b^2} = ac$

Vedclass · Answer

(c) Let first term of $G.P.$ $ = A$ and common ratio $ = r$

We know that ${n^{th}}$ term of $G.P. =$ $A{r^{n - 1}}$

Now ${t_4} = a = A{r^3},\;{t_7} = b = A{r^6}$and ${t_{10}} = c = A{r^9}$

Relation ${b^2} = ac$ is true because ${b^2} = {(A{r^6})^2} = {A^2}{r^{12}}$

and $ac = (A{r^3})(A{r^9}) = {A^2}{r^{12}}$

Aliter : As we know, if $p,q,r$ in $A.P.$,

then $p^{th},q^{th},r^{th}$ terms of a $G.P.$ are always in $G.P.$,

therefore, will be in $G.P.$

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

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