Let a and b be two distinct positive real num | vedclass

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

Question

(C) For the $1^{	ext{st}}$ $GP$: Let the common ratio be $r_1$. Given $t_1 = a$ and $t_3 = b = a r_1^2$,so $r_1^2 = \frac{b}{a}$.The $11^{	ext{th}}$

Vedclass · Accepted Answer

$21$

Vedclass · Answer

(C) For the $1^{	ext{st}}$ $GP$: Let the common ratio be $r_1$. Given $t_1 = a$ and $t_3 = b = a r_1^2$,so $r_1^2 = \frac{b}{a}$.The $11^{	ext{th}}$ term is $t_{11} = a r_1^{10} = a (r_1^2)^5 = a \left(\frac{b}{a}ight)^5$.For the $2^{	ext{nd}}$ $GP$: Let the common ratio be $r_2$. Given $T_1 = a$ and $T_5 = b = a r_2^4$,so $r_2^4 = \frac{b}{a}$,which implies $r_2 = \left(\frac{b}{a}ight)^{1/4}$.The $p^{	ext{th}}$ term is $T_p = a r_2^{p-1} = a \left(\frac{b}{a}ight)^{\frac{p-1}{4}}$.Given $t_{11} = T_p$,we have $a \left(\frac{b}{a}ight)^5 = a \left(\frac{b}{a}ight)^{\frac{p-1}{4}}$.Equating the exponents,$5 = \frac{p-1}{4}$,which gives $p-1 = 20$,so $p = 21$.

Let $a$ and $b$ be two distinct positive real numbers. Let the $11^{\text{th}}$ term of a $GP$,whose first term is $a$ and third term is $b$,be equal to the $p^{\text{th}}$ term of another $GP$,whose first term is $a$ and fifth term is $b$. Then $p$ is equal to:

Similar Questions

How many terms of the $G.P.$ $3, 3^{2}, 3^{3}, \dots$ are needed to give the sum $120$?

If three numbers are in $G.P.$,then their logarithms will be in

If the roots of the equation $8 x^3+6 p x^2+3 q x-27=0$ are in a geometric progression,then $q^2+9 p^2+6 p q+q/p=$

The sum of some terms of a $G.P.$ is $315$,whose first term and the common ratio are $5$ and $2$ respectively. Find the last term and the number of terms.

The number of bacteria in a certain culture doubles every hour. If there were $30$ bacteria present in the culture originally,how many bacteria will be present at the end of $2^{\text{nd}}$ hour,$4^{\text{th}}$ hour and $n^{\text{th}}$ hour?

Vedclass Test Series

Exam Paper Generator

Online Exam Module