If three successive terms of a G.P. with comm | vedclass

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

Question

(A) Let the three successive terms of the $G.P.$ be $a, ar, ar^2$ where $a > 0$ and $r > 1$.For these to be sides of a triangle,the sum of any two sid

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Let the three successive terms of the $G.P.$ be $a, ar, ar^2$ where $a > 0$ and $r > 1$.For these to be sides of a triangle,the sum of any two sides must be greater than the third side.$a + ar > ar^2 \implies 1 + r > r^2 \implies r^2 - r - 1 The roots of $r^2 - r - 1 = 0$ are $r = \frac{1 \pm \sqrt{5}}{2}$.Since $r > 1$,the condition $r^2 - r - 1 Given $\sqrt{5} \approx 2.236$,we have $\frac{1 + 2.236}{2} = 1.618$.So,$1 Then,$[r] = 1$.For $[-r]$,since $1 The greatest integer less than or equal to $-r$ is $[-r] = -2$.Therefore,$3[r] + [-r] = 3(1) + (-2) = 3 - 2 = 1$.

If three successive terms of a $G.P.$ with common ratio $r$ $(r > 1)$ are the lengths of the sides of a triangle,and $[r]$ denotes the greatest integer less than or equal to $r$,then $3[r] + [-r]$ is equal to:

Similar Questions

The roots of the equation $x^3-14x^2+56x-64=0$ are in

The geometric mean of $n$ positive terms $x_1, x_2, \dots, x_n$ is equal to:

If the first term of a $G.P.$ $a_1, a_2, a_3, \dots$ is unity such that $4a_2 + 5a_3$ is least,then the common ratio of the $G.P.$ is

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.

$0.14189189189...$ can be expressed as a rational number.

Vedclass Test Series

Exam Paper Generator

Online Exam Module