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Ex 9.3, 17 - If 4th, 10th and 16th terms of a GP are x, y, z - Geometric Progression(GP): Formulae based

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Ex 9.3, 17 If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P. We know that an = arn – 1 where an = nth term of GP n is the number of terms a is the first term r is the common ratio Here, 4th term is x i.e. a4 = x Putting n = 4 in an formula x = ar4 – 1 x = ar3 Also, 10th term is y i.e. a10 = y Putting n = 10 in an formula y = ar10 – 1 y = ar9 Also, 16th term is z i.e. a16 = z Putting n = 16 in an formula z = ar16 – 1 z = ar15 We need to show x, y, z are in GP i.e. we need to show 𝑦/𝑥 = 𝑧/𝑦 Calculating 𝑦/𝑥 𝑦/𝑥 Putting y = ar9 & x = ar3 = 𝑎𝑟9/𝑎𝑟3 = r9 – 3 = r6 Now calculating 𝑧/𝑦 𝑧/𝑦 putting z = ar15 & y = ar9 = 𝑎𝑟15/𝑎𝑟9 = r15 – 9 = r6 Thus, 𝑧/𝑦 = r6 , & 𝑦/𝑥 = r6 Hence 𝑦/𝑥 = 𝑧/𝑦 ∴ x, y, z are in G.P Hence proved

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