(D) If $a, b, c$ are in $A.P.$,then $2b = a + c$. If $a, b, c$ are in $G.P.$,then $b^2 = ac$. From the first equation,$c = 2b - a$. Substituting this

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

(D) If $a, b, c$ are in $A.P.$,then $2b = a + c$. If $a, b, c$ are in $G.P.$,then $b^2 = ac$. From the first equation,$c = 2b - a$. Substituting this into the second equation: $b^2 = a(2b - a)$. $b^2 = 2ab - a^2$. $a^2 - 2ab + b^2 = 0$. $(a - b)^2 = 0$. This implies $a = b$. Since $a = b$,substituting into $2b = a + c$ gives $2a = a + c$,which implies $a = c$. Therefore,$a = b = c$.

Class 11 Mathematics Sequences and Series Relation between A.P., G.P.

Medium

If $a, b, c$ are in both Arithmetic Progression $(A.P.)$ and Geometric Progression $(G.P.)$,then......

A
$a = b \neq c$
B
$a \neq b = c$
C
$a \neq b \neq c$
D
$a = b = c$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Sequences and Series

Subtopic

Relation between A.P., G.P.

If the first and $(2n - 1)^{th}$ terms of an $A.P.$,$G.P.$,and $H.P.$ are equal and their $n^{th}$ terms are respectively $a, b$ and $c$,then:

DifficultIIT 1985

View Solution

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

Medium

View Solution

If $x, y, z$ are in Arithmetic Progression $(AP)$ and $x, y, t$ are in Geometric Progression $(GP)$,then in which progression are $x, x - y, t - z$?

Difficult

View Solution

If the $A.M.$ of two numbers is greater than the $G.M.$ of the numbers by $2$ and the ratio of the numbers is $4:1$,then the numbers are

Medium

View Solution

If the arithmetic mean of two positive numbers is $A$,their geometric mean is $G$,and their harmonic mean is $H$,then $H$ is equal to:

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $a, b, c$ are in both Arithmetic Progression $(A.P.)$ and Geometric Progression $(G.P.)$,then......

Similar Questions

If the first and $(2n - 1)^{th}$ terms of an $A.P.$,$G.P.$,and $H.P.$ are equal and their $n^{th}$ terms are respectively $a, b$ and $c$,then:

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

If $x, y, z$ are in Arithmetic Progression $(AP)$ and $x, y, t$ are in Geometric Progression $(GP)$,then in which progression are $x, x - y, t - z$?

If the $A.M.$ of two numbers is greater than the $G.M.$ of the numbers by $2$ and the ratio of the numbers is $4:1$,then the numbers are

If the arithmetic mean of two positive numbers is $A$,their geometric mean is $G$,and their harmonic mean is $H$,then $H$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module