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Ex 5.2, 9 - If 3rd and 9th terms of an AP are 4 and -8 - Finding n

  1. Chapter 5 Class 10th Arithmetic Progressions
  2. Serial order wise
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Ex 5.2 ,9 If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero. We know that an = a + (n – 1) d From (1) & (2) 4 – 2d = – 8d – 8 – 2d + 8d = – 8 – 4 6d = – 12 d = (−12)/6 d = – 2 Putting value of d in (2) a = 4 – 2d = 4 – 2 × ( – 2) = 4 + 4 = 8 We need to cheek whether 301 is a term of AP Lets assume it is nth term of AP So, an = 0 , Also, a = 8 & d = – 2 We know that an = a + (n – 1)d Putting values 0 = 8 + (n – 1) × – 2 0 = 8 + n × ( – 2) – 1 × (– 2) 0 = 8 – 2n + 2 0 = 10 – 2n 2n = 10 n = 10/2 n = 5 ∴ 5th term of AP is 0

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