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

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

If $A = 1 + {r^z} + {r^{2z}} + {r^{3z}} + .......\infty $, then the value of $r$ will be

An $A.P.$, a $G.P.$ and a $H.P.$ have the same first and last terms and the same odd number of terms. The middle terms of the three series are in

The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$, will be

The numbers $(\sqrt 2 + 1),\;1,\;(\sqrt 2 - 1)$ will be in

If the first and the $n^{\text {th }}$ term of a $G.P.$ are $a$ and $b$, respectively, and if $P$ is the product of $n$ terms, prove that $P^{2}=(a b)^{n}$