Let $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ be in G. P. with common ratio r, where
$a \neq 0$ and $0 first three terms of an A. P., then the $4^{\text {th }}$ term of this A. P. is :
$\frac{7}{3} a$
$a$
$\frac{2}{3} a$
$5 \mathrm{a}$
Correct Option: , 2
$\mathrm{b}=\mathrm{ar}$
$\mathrm{c}=\mathrm{ar}{ }^{2}$
$3 \mathrm{a}, 7 \mathrm{~b}$ and $15 \mathrm{c}$ are in A.P.
$\Rightarrow 14 b=3 a+15 c$
$\Rightarrow 14(a r)=3 a+15 a r^{2}$
$\Rightarrow 14 r=3+15 r^{2}$
$\Rightarrow 15 r^{2}-14 r+3=0 \quad \Rightarrow(3 r-1)(5 r-3)=0$
$r=\frac{1}{3}, \frac{3}{5}$
Only acceptable value is $\mathrm{r}=\frac{1}{3}$, because
$r \in\left(0, \frac{1}{2}\right]$
$\therefore \mathrm{c} . \mathrm{d}=7 \mathrm{~b}-3 \mathrm{a}=7 \mathrm{ar}-3 \mathrm{a}=\frac{7}{3} \mathrm{a}-3 \mathrm{a}=-\frac{2}{3} \mathrm{a}$
$\therefore 4^{\text {th }}$ term $=15 \mathrm{c}-\frac{2}{3} \mathrm{a}=\frac{15}{9} \mathrm{a}-\frac{2}{3} \mathrm{a}=\mathrm{a}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,