Question 8 - Examples - Chapter 8 Class 11 Sequences and Series

Last updated at April 16, 2024 by

Example 21 - If pth, qth, rth sth terms of AP are in GP - Examples

Example 21 - Chapter 9 Class 11 Sequences and Series - Part 2
Example 21 - Chapter 9 Class 11 Sequences and Series - Part 3
Example 21 - Chapter 9 Class 11 Sequences and Series - Part 4

Transcript

Question 8 If pth, qth, rth and sth terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P. We know that the nth term of AP is a + (n – 1)d i.e. an = a + (n – 1)d It is given that ap, aq, ar & as in GP i.e. their common ratio is same So,𝑎_𝑞/𝑎_𝑝 = (ar )/qq = 𝑎𝑠/𝑎𝑟 We need to show (p – q), (q – r), (r – s) are in GP i.e. we need to show their common ratio is same i.e. we need to show (q − r )/(p − q) = (r − s )/(q − r) It is given (aq )/qp = (ar )/qq = (as )/ar From (A) & (B) (𝑞 − 𝑟)/(𝑝 − 𝑞) = (𝑟 − 𝑠)/(𝑞 − 𝑟) Hence (p – q), (q – r), (r – s) are in GP Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.