Last updated at May 29, 2018 by Teachoo

Transcript

Ex 5.3 ,11 If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly find the 3rd, the10th and the nth terms. Given Sn = 4n – n2 Taking n = 1 S1 = 4 ×1−12 = 4 – 1 = 3 So, Sum of first term of AP is 3 But sum of first term will be the first term So, First term = a = 3 Taking n = 2 in Sn S2 = 4×2−2^2 S2 = 8 – 4 S2 = 4 ∴ Sum of first 2 terms is 4 Finding 2nd term Sum of first 2 terms is 4 First term + Second term = 4 3 + a2 = 4 a2 = 4 – 3 a2 = 1 Hence in AP , First term = a = 3 Common difference = d = Second term – First term = 1 – 3 = –2 We need to find 3rd, 10th and nth term We know that an = a + (n – 1) d Third term a3 = a + (3 – 1) d = a + 2d = 3 + 2 ×(−2) = 3 – 4 = – 1 10th term a10 = a + (10 – 1) d = a + 9d = 3 + 9 × – 2 = 3 – 18 = – 15 nth term an = a + (n – 1)d = 3 + (n – 1) × ( – 2) = 3 + n (–2) – 1 ×( – 2) = 3 –2n + 2 = 5 – 2n

Chapter 5 Class 10 Arithmetic Progressions

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.