Learn all Concepts of Chapter 5 Class 10 (with VIDEOS). Check - Arithmetic Progressions - Class 10

Last updated at March 19, 2021 by Teachoo

Transcript

Ex 5.1, 1 In which of the following situations, does the list of numbers involved make as arithmetic progression and why? The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km. Taxi fare for 1 km = Rs 15 Taxi fare for 2 km = 15 + 8 = Rs 23 Taxi fare for 3 km = 23 + 8 = Rs 31 Therefore, Series is 15, 23, 31 …….. Difference between 2nd term and 1st term = 23 – 15 = 8 Difference between 3rd term and 2nd term = 31 – 23 = 8 Since difference is same, it is an AP Ex 5.1, 1 (ii) The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time. Let Volume of cylinder be 16 litres Air removed by pump = 1/4 of 16 = 1/4 × 16 = 4 litres Air present after first removal = 16 – 4 = 12 litres Air again removed by pump = 1/4 of 12 = 1/4 × 12 = 3 litres Air present after second removal = 12 – 3 = 9 litres The amount of air present in cylinder is the series 16, 12 , 9,……. Difference between 2nd and 1st term = 12 – 16 = –4 Difference between 3rd and 2nd term = 9 – 12 = –3 Since Difference is not same, it is not an AP Ex 5.1, 1 (iii) The cost of digging a well after every metre of digging, when it costs Rs 150 for the first metre and rises by Rs 50 for each subsequent metre. Cost of digging first metre = Rs 150 Cost of digging 2 metres = Rs 150 + Rs 50 = Rs 200 Cost of diggings 3 metre = Rs 200 + Rs 50 = Rs 250 So, the series is 150, 200, 250 ………. Difference between second and first term = 200 – 150 = 50 Difference between third and second term = 250 – 200 = 50 Since difference is same, it is an AP Ex 5.1, 1 (iv) The amount of money in the account every year, when Rs 10000 is deposited at compound interest at 8% per annum. Original amount = Rs 10,000 For Compound Interest, we use the formula Amount = P(1+𝑅/100)^𝑇 Hence the amount of money in account every year is a series 10800,11664, 12597.12,….. Difference between second and first term = 11664 – 10800 = 864 Difference between third and second term = 12697.12 – 11664 = 933.12 Since difference is not same 864 ≠ 933.12 It is not an AP

Class 10

Important Questions for Exam - Class 10

- Chapter 1 Class 10 Real Numbers
- Chapter 2 Class 10 Polynomials
- Chapter 3 Class 10 Pair of Linear Equations in Two Variables
- Chapter 4 Class 10 Quadratic Equations
- Chapter 5 Class 10 Arithmetic Progressions
- Chapter 6 Class 10 Triangles
- Chapter 7 Class 10 Coordinate Geometry
- Chapter 8 Class 10 Introduction to Trignometry
- Chapter 9 Class 10 Some Applications of Trignometry
- Chapter 10 Class 10 Circles
- Chapter 11 Class 10 Constructions
- Chapter 12 Class 10 Areas related to Circles
- Chapter 13 Class 10 Surface Areas and Volumes
- Chapter 14 Class 10 Statistics
- Chapter 15 Class 10 Probability

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.