Ex 9.3, 6 - For what values of x, -2/7, x, -7/2 are in GP - Ex 9.3

Ex 9.3, 6 - Chapter 9 Class 11 Sequences and Series - Part 2
Ex 9.3, 6 - Chapter 9 Class 11 Sequences and Series - Part 3

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Transcript

Ex 8.2,6 For what values of x, the numbers (−2)/7, x, (−7)/2 are in G.P? Since (−2)/7, x, (−7)/2 are in GP So common ratio will be same Common ratio (r) = (𝑆𝑒𝑐𝑜𝑛𝑑 𝑡𝑒𝑟𝑚 )/(𝐹𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚) = 𝑥/((−2)/7) = 7𝑥/(−2) Also, Common ratio (r) = (𝑇ℎ𝑖𝑟𝑑 𝑡𝑒𝑟𝑚 )/(𝑆𝑒𝑐𝑜𝑛𝑑 𝑡𝑒𝑟𝑚) = ((−7)/2)/𝑥 = (−7)/2𝑥 From (1) & (2) 7𝑥/(−2) = (−7)/2𝑥 7x × 2x = (-7) × (-2) 14x2 = 14 x2 = 14/14 x2 = 1 x = ± √1 x = ±1 So, x = 1 or x = -1 GP is (−2)/7, x, (−7)/2 For x = 1, GP is (−2)/7, 1, (−7)/2 For x = –1, GP is (−2)/7, –1, (−7)/2 Hence possible numbers in GP are (−2)/7, 1, (−7)/2 or (−2)/7, –1, (−7)/2

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.