Question 9 - End-of-Chapter Exercises - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

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Question 9 Find the smallest value of 𝑛 such that the sum of the first 𝑛 natural numbers is greater than 1,000. Given that Sum of first n natural numbers > 1,000 𝑆_𝑛>1000 Putting formula (𝒏(𝒏 + 𝟏))/𝟐>𝟏𝟎𝟎𝟎 Multiplying 2 on right side 𝑛(𝑛 + 1)>2 × 1000 𝒏(𝒏+𝟏) >𝟐𝟎𝟎𝟎 We can test some values of n now Now, For n = 10, 10 × 11 = 110 For n = 20, 20 × 21 = 420 For n = 30, 30 × 31 = 930 For n = 40, 40 × 41 = 1,640 For n = 50, 50 × 51 = 2,550 Thus, n is between 40 and 50 Let’s try 45 For n = 45, 45 × 46 = 2,070 This product is greater than 2,000. So, it would work, but let’s see for n = 44 as well (to check if n = 44 is smallest) So, we try n = 44 For n = 44, 44 × 45 = 1,980 Thus, smallest value of n is 45