Ex 5.2, 13 - How many three digit numbers are divisible by 7 - Ex 5.2

  1. Chapter 5 Class 10 Arithmetic Progressions
  2. Serial order wise
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Ex 5.2 ,13 How many three digit numbers are divisible by 7 Numbers divisible by 7 are 7, 14, 21,28, …….. So the series starts with 105 and ends with 994 So, series will be 105, 112, 119, 126 …. 994 Since difference is same, it is an AP Last term of this series is 994 We need to find number of terms, i.e., n an = a + (n – 1) d Here an = 994 , a = 105 , d= 7 Putting values in formula an = a + (n – 1) d 994 = 105 + (n – 1) × 7 994 = 105 + n (7) – 1 × (7) 994 = 105 + 7n – 7 994 – 105 + 7 = 7n 896 = 7n 896/7 = n 128 = n n = 128 Therefore, 128 3-digit numbers are divisible by 7

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