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

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Ex 9.3,6 For what values of x, the numbers (โˆ’2)/7, x, (โˆ’7)/2 are in G.P? Since (โˆ’2)/7, x, (โˆ’7)/2 are in GP So common ratio will be same Common ratio (r) = (๐‘†๐‘’๐‘๐‘œ๐‘›๐‘‘ ๐‘ก๐‘’๐‘Ÿ๐‘š )/(๐น๐‘–๐‘Ÿ๐‘ ๐‘ก ๐‘ก๐‘’๐‘Ÿ๐‘š) = ๐‘ฅ/((โˆ’2)/7) = 7๐‘ฅ/(โˆ’2) Also, Common ratio (r) = (๐‘‡โ„Ž๐‘–๐‘Ÿ๐‘‘ ๐‘ก๐‘’๐‘Ÿ๐‘š )/(๐‘†๐‘’๐‘๐‘œ๐‘›๐‘‘ ๐‘ก๐‘’๐‘Ÿ๐‘š) = ((โˆ’7)/2)/๐‘ฅ = (โˆ’7)/2๐‘ฅ From (1) & (2) 7๐‘ฅ/(โˆ’2) = (โˆ’7)/2๐‘ฅ 7x ร— 2x = (-7) ร— (-2) 14x2 = 14 x2 = 14/14 x2 = 1 x = ยฑ โˆš1 x = ยฑ1 So, x = 1 or x = -1 GP is (โˆ’2)/7, x, (โˆ’7)/2 For x = 1, GP is (โˆ’2)/7, 1, (โˆ’7)/2 For x = โ€“1, GP is (โˆ’2)/7, โ€“1, (โˆ’7)/2 Hence possible numbers in GP are (โˆ’2)/7, 1, (โˆ’7)/2 or (โˆ’2)/7, โ€“1, (โˆ’7)/2

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