If a, b, c are in A.P.,then 2^{ax + 1}, 2^{bx | vedclass

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

Question

(D) Given that $a, b, c$ are in $A.P.$,we have $b - a = c - b$.Let the terms be $T_1 = 2^{ax + 1}$,$T_2 = 2^{bx + 1}$,and $T_3 = 2^{cx + 1}$.For these

Vedclass · Accepted Answer

$G.P.$ for all $x 
e 0$

Vedclass · Answer

(D) Given that $a, b, c$ are in $A.P.$,we have $b - a = c - b$.Let the terms be $T_1 = 2^{ax + 1}$,$T_2 = 2^{bx + 1}$,and $T_3 = 2^{cx + 1}$.For these terms to be in $G.P.$,the ratio $\frac{T_2}{T_1}$ must equal $\frac{T_3}{T_2}$.$\frac{T_2}{T_1} = \frac{2^{bx + 1}}{2^{ax + 1}} = 2^{(b - a)x}$.$\frac{T_3}{T_2} = \frac{2^{cx + 1}}{2^{bx + 1}} = 2^{(c - b)x}$.Since $b - a = c - b$,it follows that $2^{(b - a)x} = 2^{(c - b)x}$ for all $x 
e 0$.Thus,the terms form a $G.P.$ for all $x 
e 0$.

If $a, b, c$ are in $A.P.$,then $2^{ax + 1}, 2^{bx + 1}, 2^{cx + 1}$ for $x \ne 0$ are in

Similar Questions

The number of terms common between the two series $2 + 5 + 8 + \dots$ up to $50$ terms and the series $3 + 5 + 7 + 9 + \dots$ up to $60$ terms is:

If $a, b, c$ are three unequal numbers such that $a, b, c$ are in $A.P.$ and $b - a, c - b, a$ are in $G.P.$,then $a : b : c$ is

If $9$ arithmetic means $(A.M.s)$ and $9$ harmonic means $(H.M.s)$ are inserted between $2$ and $3$,and if the harmonic mean $H$ corresponds to the arithmetic mean $A$ (i.e.,the $j^{th}$ $A.M.$ and $j^{th}$ $H.M.$),then $A + \frac{6}{H} = $

If $a, b, c$ are in $G.P.$ and $a + x, b + x, c + x$ are in $H.P.$,then the value of $x$ is ($a, b, c$ are distinct numbers).

Let ${a_1, a_2, \dots, a_{10}}$ be in $A.P.$ and ${h_1, h_2, \dots, h_{10}}$ be in $H.P.$ If ${a_1 = h_1 = 2}$ and ${a_{10} = h_{10} = 3}$,then the value of ${a_4 h_7}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module