Example 4 - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

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Example 4 Find the first four terms of the sequence given by the recursive rule 𝑠_1=3,𝑠_𝑛=𝑠_(𝑛−1) (𝑠_(𝑛−1)−1) for 𝑛≥2. First, let’s find first four terms i.e. 𝒔_𝟏, 𝒔_𝟐, 𝒔_𝟑, 𝒔_𝟒 Given First term = 𝒔_𝟏 = 3 Second term = 𝑠_2 = 𝑠_(2−1) (𝑠_(2−1)−1) = 𝒔_𝟏 (𝒔_𝟏−𝟏) = 3 × (3 – 1) = 3 × 2 = 6 Third term = 𝑠_3 = 𝑠_(3−1) (𝑠_(3−1)−1) = 𝒔_𝟐 (𝒔_𝟐−𝟏) = 6 × (6 – 1) = 6 × 5 = 30 Fourth term = 𝑠_4 = 𝑠_(4−1) (𝑠_(4−1)−1) = 𝒔_𝟑 (𝒔_𝟑−𝟏) = 30 × (30 – 1) = 30 × 29 = 870 Thus, first four terms of the sequence are 3, 6, 30, 870