Check sibling questions

Ex 5.3, 3 - Chapter 5 Class 10 Arithmetic Progressions - Part 19

Ex 5.3, 3 - Chapter 5 Class 10 Arithmetic Progressions - Part 20
Ex 5.3, 3 - Chapter 5 Class 10 Arithmetic Progressions - Part 21
Ex 5.3, 3 - Chapter 5 Class 10 Arithmetic Progressions - Part 22

This video is only available for Teachoo black users


Transcript

Ex 5.3, 3 In an AP (viii) Given an = 4, d = 2, Sn = βˆ’14, find n and a. Given an = 4, d = 2, Sn = –14 Since there are n terms, 𝑙 = an = 4 We use the formula Sn = 𝒏/𝟐 (𝒂+𝒍) Putting Sn = βˆ’14, 𝑙 = an = 4 –14 = 𝑛/2 (π‘Ž+4) –14 Γ— 2 =𝑛(π‘Ž+4) –28 = n (a + 4) (βˆ’28)/(π‘Ž + 4)=𝑛 n = (βˆ’πŸπŸ–)/(𝒂 + πŸ’) Also we know that an = a + (n – 1) d Putting an = 4 , d = 2 4 = a + (n – 1) Γ— 2 4 = a + 2n – 2 4 + 2 = a + 2n 6 = a + 2n Putting n = (βˆ’ πŸπŸ–)/(𝒂 + πŸ’) 6 = a + 2((βˆ’ 28)/(π‘Ž + 4)) 6 = a βˆ’ 56/(π‘Ž + 4) 6 = (π‘Ž(π‘Ž + 4) βˆ’ 56)/(π‘Ž + 4) 6 = (π‘Ž2 + 4π‘Ž βˆ’ 56)/(π‘Ž + 4) 6 (a + 4) = a2 + 4a – 56 6a + 24 = a2 4a – 56 0 = a2 + 4a – 56 – 6a – 24 0 = a2 – 2a – 80 a2 – 2a – 80 = 0 a2 – 10a + 8a– 80 = 0 a (a – 10) + 8 (a – 8) = 0 (a – 10) (a + 8) = 0 So, a = 10 or a = –8 Taking a = 10 n = (βˆ’ 28)/(π‘Ž + 4) n = (βˆ’ 28)/(10 + 4) n = (βˆ’ 28)/14 n = –2 Since n is number of terms, it cannot be negative So, n = –2 is not possible ∴ a = 10 is not possible Taking a = – 8 n = (βˆ’ 28)/(π‘Ž + 4) n = (βˆ’ 28)/(βˆ’ 8 + 4) n = (βˆ’ 28)/( βˆ’ 4) n = 7 So, n = 7

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.