The $2^{\text {nd }}$ and $5^{\text {th }}$ terms of a GP are $\frac{-1}{2}$ and $\frac{1}{16}$ respectively. Find the sum of $n$ terms GP up to 8 terms.
$2^{\text {nd }}$ term $=a r^{2-1}=a r^{1}$
$5^{\text {th }}$ term $=a r^{5-1}=a r^{4}$
Dividing the $5^{\text {th }}$ term using the $3^{\text {rd }}$ term
$\frac{a r^{4}}{a r}=\frac{\frac{1}{16}}{\frac{-1}{2}}$
$r^{3}=-\frac{1}{8}$
$\therefore r=-\frac{-1}{2}$
∴ a = 1
Sum of a G.P. series is represented by the formula $S_{n}=a \frac{1-r^{n}}{1-r}$ when |r|<1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.
n = 8 terms
$\mathrm{S}_{\mathrm{n}}=1 \times \frac{1-\frac{-1^{8}}{2}}{1-\frac{-1}{2}}$
$\Rightarrow \mathrm{S}_{\mathrm{n}}=\frac{1-\frac{1}{256}}{\frac{3}{2}}$
$\Rightarrow \mathrm{S}_{\mathrm{n}}=\frac{\frac{255}{256}}{\frac{3}{2}}$
$\therefore \mathrm{S}_{\mathrm{n}}=\frac{170}{256}$
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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,