If in the expansion of (1 + x)n, the coefficients of three consecutive terms are 56, 70 and 56, then find n and the position of the terms of these coefficients.
Suppose $r^{t h},(r+1)^{t h}$ and $(r+2)^{t h}$ terms are the three consecutive terms.
Their respective coefficients are ${ }^{n} C_{r-1},{ }^{n} C_{r}$ and ${ }^{n} C_{r+1}$.
We have:
${ }^{n} C_{r-1}={ }^{n} C_{r+1}=56$
$\Rightarrow r-1+r+1=n \quad\left[\right.$ If ${ }^{n} C_{r}={ }^{n} C_{s} \Rightarrow r=s$ or $\left.r+s=n\right]$
$\Rightarrow 2 r=n$
$\Rightarrow r=\frac{n}{2}$
Now,
${ }^{n} C_{\frac{n}{2}}=70$ and ${ }^{n} C_{\left(\frac{n}{2}-1\right)}=56$
$\Rightarrow \frac{{ }^{n} C_{\left(\frac{n}{2}-1\right)}}{{ }^{n} C_{\frac{n}{2}}}=\frac{56}{70}$
$\Rightarrow \frac{\frac{n}{2}}{\left(\frac{n}{2}+1\right)}=\frac{8}{10}$
$\Rightarrow 5 n=4 n+8$
$\Rightarrow n=8$
So, $r=\frac{n}{2}=4$
Thus, the required terms are 4 th, 5 th and 6 th.
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- 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
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- Chemical Effects of Electric Current,