(A) Given that $\frac{1}{4}, a, b, \frac{1}{19}$ are in $H.P.$Therefore,their reciprocals $4, \frac{1}{a}, \frac{1}{b}, 19$ are in $A.P.$Let the $A.P.

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

(A) Given that $\frac{1}{4}, a, b, \frac{1}{19}$ are in $H.P.$Therefore,their reciprocals $4, \frac{1}{a}, \frac{1}{b}, 19$ are in $A.P.$Let the $A.P.$ be $4, 4+d, 4+2d, 4+3d$.Here,$4+3d = 19 \implies 3d = 15 \implies d = 5$.Thus,the terms are $4, 4+5, 4+10, 19$,which are $4, 9, 14, 19$.Comparing the terms,$\frac{1}{a} = 9 \implies a = \frac{1}{9}$ and $\frac{1}{b} = 14 \implies b = \frac{1}{14}$.

Class 11 Mathematics Sequences and Series Harmonic progression

Medium

If $\frac{1}{4}, a, b, \frac{1}{19}$ form a $H.P.$,then the values of $a$ and $b$ are respectively:

MHT CET 2020 All MHT CET

A
$\frac{1}{9}, \frac{1}{14}$
B
$\frac{1}{5}, \frac{1}{7}$
C
$\frac{1}{12}, \frac{1}{15}$
D
$\frac{1}{11}, \frac{1}{17}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Sequences and Series

Subtopic

Harmonic progression

Previous Year

MHT CET 2020 Paper All MHT CET years →

Given that the roots of $x^3+3px^2+3qx+r=0$ are in harmonic progression,then:

EasyTS EAMCET 2018

View Solution

If $X = \sum_{n=0}^\infty a^n$,$Y = \sum_{n=0}^\infty b^n$,and $Z = \sum_{n=0}^\infty c^n$,where $a, b, c$ are in arithmetic progression and $|a| < 1, |b| < 1, |c| < 1$,then $X, Y, Z$ are in . . . . progression.

Difficult

View Solution

If $a, b, c$ are in $H.P.$,then for all $n \in N$ $(n > 1)$,the true statement is:

Difficult

View Solution

The $4^{th}$ term of a $H.P.$ is $\frac{3}{5}$ and $8^{th}$ term is $\frac{1}{3},$ then its $6^{th}$ term is

Easy

View Solution

If $a, b, c$ are in $H.P.$,then the value of $\left( \frac{1}{b} + \frac{1}{c} - \frac{1}{a} \right) \left( \frac{1}{c} + \frac{1}{a} - \frac{1}{b} \right)$ is

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 $\frac{1}{4}, a, b, \frac{1}{19}$ form a $H.P.$,then the values of $a$ and $b$ are respectively:

Similar Questions

Given that the roots of $x^3+3px^2+3qx+r=0$ are in harmonic progression,then:

If $X = \sum_{n=0}^\infty a^n$,$Y = \sum_{n=0}^\infty b^n$,and $Z = \sum_{n=0}^\infty c^n$,where $a, b, c$ are in arithmetic progression and $|a| < 1, |b| < 1, |c| < 1$,then $X, Y, Z$ are in . . . . progression.

If $a, b, c$ are in $H.P.$,then for all $n \in N$ $(n > 1)$,the true statement is:

The $4^{th}$ term of a $H.P.$ is $\frac{3}{5}$ and $8^{th}$ term is $\frac{1}{3},$ then its $6^{th}$ term is

If $a, b, c$ are in $H.P.$,then the value of $\left( \frac{1}{b} + \frac{1}{c} - \frac{1}{a} \right) \left( \frac{1}{c} + \frac{1}{a} - \frac{1}{b} \right)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module