The sum of the 3^{rd} and the 4^{th} terms of | vedclass

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Question

Let $a, ar$ and $a{r^2}$ be the first three terms of $G.P$

According to the question

$a\left( {ar} \right)\left( {a{r^2}} \right) = 1000 \R

Vedclass · Accepted Answer

$320$

Vedclass · Answer

Let $a, ar$ and $a{r^2}$ be the first three terms of $G.P$

According to the question

$a\left( {ar} ight)\left( {a{r^2}} ight) = 1000 \Rightarrow {\left( {ar} ight)^3} = 1000 \Rightarrow ar = 10$

and $a{r^2} + a{r^3} = 60 \Rightarrow ar\left( {r + {r^2}} ight) = 60$

$ \Rightarrow {r^2} + r - 6 = 0$

$ \Rightarrow r = 2, - 3$

$a = 5,a =  - \frac{{10}}{3}$    (reject)

Hence, ${T_7} = a{r^6} = 5{\left( 2 ight)^6} = 5 	imes 64 = 320$

The sum of the $3^{rd}$ and the $4^{th}$ terms of a $G.P.$ is $60$ and the product of its first three terms is $1000$. If the first term of this $G.P.$ is positive, then its $7^{th}$ term is

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