Ex 9.3, 1 - Find 20th and nth terms of GP 5/2, 5/4, 5/8 - Geometric Progression(GP): Formulae based

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Ex 9.3, 1 Find the 20th and nth terms of the G.P. 5/2, 5/4, 5/8,…. G.P. is 5/2, 5/4, 5/8,…. 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, First term a = 5/2 Common ratio r = (5/4)/(5/2) = 5/4 × 2/5 = 1/2 We need to find nth term, nth term of GP = an = arn-1 Putting a = 5/2 , d = 1/2 = 5/2 (1/2)^(𝑛−1) = 5/2 (1/2^(𝑛−1) ) = (5/(〖2 (2〗^(𝑛−1)))) = 5/(2)"n − 1 + 1" = 5/2^𝑛 Hence, the nth term of GP is 5/2^𝑛 For 20th term of GP Putting n = 20 in an a20 = 5/2^20 Thus, 20th term of GP is 5/2^20

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