Example 2 - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

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Example 2 As another example, consider the sequence that is generated by the explicit formula 𝑠_𝑛=5𝑛−2. Can you write the first 6 terms of this sequence? What is the 100th term? The 1000th term? We need to find first six terms i.e. 𝒔_𝟏, 𝒔_𝟐, 𝒔_𝟑, 𝒔_𝟒, 𝒔_𝟓,𝒔_𝟔 Given 𝑠_𝑛=5𝑛−2 Putting n = 1 in 𝒔_𝒏 𝑠_1=5(1)−2 = 5 – 2 = 3 Putting n = 2 in 𝒔_𝒏 𝑠_2=5(2)−2 = 10 – 2 = 8 Putting n = 3 in 𝒔_𝒏 𝑠_3=5(3)−2 = 15 – 2 = 13 Putting n = 4 in 𝒔_𝒏 𝑠_4=5(4)−2 = 20 – 2 = 18 Putting n = 5 in 𝒔_𝒏 𝑠_5=5(5)−2 = 25 – 2 = 23 Putting n = 6 in 𝒔_𝒏 𝑠_6=5(6)−2 = 30 – 2 = 28 Thus, first 6 terms are 3, 8, 13, 18, 23, 28 Now, we are asked What is the 100th term? The 1000th term? Now, 100th term = 𝑠_100 = 5(100)−2 = 500 – 2 = 498 1000th term = 𝑠_1000 = 5(1000)−2 = 5000 – 2 = 4,998