Ex 5.2, 5 - Find number of terms in AP (i) 7, 13, 19, .. 205 - Finding n

  1. Chapter 5 Class 10 Arithmetic Progressions
  2. Serial order wise
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Ex 5.2,5 Find the number of terms in the following AP (i) 7, 13, 19, …, 205 7, 13, 19, … 205 an = a + (n – 1) d Hence, a = 7 d = 13 – 7 = 6 an = 205 We need to find n an = a + (n – 1) d 205 = 7 + (n – 1) × 6 205 – 7 = (n – 1) × 6 198 = (n – 1) × 6 198/6 = n – 1 33 = n – 1 33 + 1 = n 34 = n n = 34 Hence there are 34 terms in the given AP Ex 5.2 ,5 Find the number of terms in the following AP (ii) 18, 151/2, 13,……….,-47 18, 15 1/2 , 13, … 47 We know that an = a + (n – 1) d Hence, an = – 47 a = 18 d = 15 1/2 – 18 = (15 × 2 +1)/2 – 18 = 31/2 – 18 = (31 − 18 × 2)/2 = (31− 36)/2 = (− 5)/2 We need to find n an = a + (n – 1) d – 47 = 18 + (n – 1) × ((− 5)/2) – 65 = (n – 1) × ((− 5)/2) (− 65 × 2)/(− 5) = (n – 1) 26 = n – 1 n – 1 = 26 n = 26 + 1 n = 27 Hence the number of terms in the given AP is 27

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