Ex 8.3, 3 - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

Transcript

Ex 8.3, 3 A sequence is given by the recursive rule 𝑡_1=2,𝑡_(𝑛+1)=3𝑡_𝑛−2 for 𝑛≥1. Which term of the sequence is 730? Let’s find the sequence from the rule First term = 𝒕_𝟏=𝟐 And, Second term 𝑡_2 = 𝟑𝒕_𝟏−𝟐 = 3 × 2 – 2 = 6 – 2 = 4 Third term 𝑡_3 = 𝟑𝒕_𝟐−𝟐 = 3 × 4 – 2 = 12 – 2 = 10 Fourth term 𝑡_4 = 𝟑𝒕_𝟑−𝟐 = 3 × 10 – 2 = 30 – 2 = 28 Now, our sequence is 2, 4, 10, 28…. Since it is neither an AP or a GP We just continue finding more terms until we get to 730 Thus, 7th term of the sequence is 730 Fifth term 𝑡_5 = 𝟑𝒕_𝟒−𝟐 = 3 × 28 – 2 = 84 – 2 = 82 Sixth term 𝑡_6 = 𝟑𝒕_𝟓−𝟐 = 3 × 82 – 2 = 246 – 2 = 244 Sevent term 𝑡_7 = 𝟑𝒕_𝟔−𝟐 = 3 × 244 – 2 = 732 – 2 = 730