A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter.
(a) Find his salary for the tenth month
(b) What is his total earnings during the first year?
Given the man’s salary in first month is 5200rs and then it increases every month by 320rs
Hence the sequence of his salary per month will be 5200, 5200 + 320, 5200 + 640…
The sequence is in AP with first term as a = 5200,
Common difference as d = 320
a) Now we have to find salary in 10th month that is 10th term of the AP
The nth term of AP is given by tn = a + (n – 1) d
Where a is the first term and d is the common difference
We have to find t10
⇒ t10 = 5200 + (10 – 1) (320)
⇒ t10 = 5200 + 2880
⇒ t10 = 8080
Hence salary in 10th month is 8080rs
b) To get the total earnings in first year we have to add first 12 terms of the sequence that is we have to find S12
The sum of first n terms of AP is given by Sn = n/2 (2a + (n – 1) d)
Where a is the first term and d is common difference
S12 = (12/2) (2 (5200) + (12 – 1) 320)
⇒ S12 = 6(10400 + 11(320))
⇒ S12 = 6(10400 + 3520)
⇒ S12 = 6(13920)
⇒ S12 = 83520
Hence his total earnings in first year is 83520rs
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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,