Virahānka–Fibonacci sequence - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

Transcript

Virahānka–Fibonacci sequence Virahāṅka–Fibonacci Numbers is the sequence 1, 2, 3, 5, 8, 13, 21, 34, . . . This sequence has a Recursive rule The rule is 𝑽_𝒏=𝑽_(𝒏−𝟏)+𝑽_(𝒏−𝟐) for n ≥ 3 Where, 𝑽_𝟏=𝟏,𝑽_𝟐=𝟐 In plain English To get the next number, add the two numbers that came right before it Let’s find some values now 3rd term = 𝑉_3 = 𝑽_𝟐+𝑽_𝟏 = 1 + 2 = 3 4th term = 𝑉_4 = 𝑽_𝟑+𝑽_𝟐 = 3 + 2 = 5 5th term = 𝑉_5 = 𝑽_𝟒+𝑽_𝟑 = 5 + 3 = 8 6th term = 𝑉_6 = 𝑽_𝟓+𝑽_𝟒 = 8 + 5 = 13 7th term = 𝑉_7 = 𝑽_𝟔+𝑽_𝟓 = 13 + 8 = 21 7th term = 𝑉_7 = 𝑽_𝟔+𝑽_𝟓 = 13 + 8 = 21 8th term = 𝑉_8 = 𝑽_𝟕+𝑽_𝟔 = 21 + 13 = 34 9th term = 𝑉_9 = 𝑽_𝟖+𝑽_𝟕 = 34 + 21 = 55 10th term = 𝑉_10 = 𝑽_𝟗+𝑽_𝟖 = 55 + 34 = 89 Thus, the Virahānka–Fibonacci Sequence is 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … Now, let’s do some questions