Question 3 - End-of-Chapter Exercises - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

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Question 3 How many three-digit numbers are divisible by 7? (Hint: All three-digit numbers divisible by 7 form an AP. Find the smallest and largest such three-digit numbers.) Numbers divisible by 7 are 7, 14, 21, 28, …….. Let’s find the smallest and largest 3-digit number divisible by 7 Smallest 3 digit number 𝟏𝟎𝟎/𝟕 = 14𝟐/𝟕 101/7 = 143/7 102/7 = 144/7 𝟏𝟎𝟓/𝟕 = 15 ∴ Smallest number is 105 Largest 3 digit number 𝟗𝟗𝟗/𝟕 = 142𝟓/𝟕 998/7 = 1424/7 997/7 = 1423/7 𝟗𝟗𝟒/𝟕 = 142 ∴ Largest number is 994 Now, our 3-digit numbers divisible by 7 form an AP The AP is 105, 112, 119, 126 …. 994 Where First term = a = 105 Common difference = d = 7 Last term = an = 994 We need to find number of terms, i.e., n 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, there are 128 3-digit numbers are divisible by 7