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Ex 9.1, 14 - The Fibonacci sequence is 1 = a1 = a2 - Finding Sequences

Ex 9.1, 14 - Chapter 9 Class 11 Sequences and Series - Part 2
Ex 9.1, 14 - Chapter 9 Class 11 Sequences and Series - Part 3
Ex 9.1, 14 - Chapter 9 Class 11 Sequences and Series - Part 4

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Ex9.1 , 14 The Fibonacci sequence is defined by 1 = a1 = a2 and an = anโ€“1+anโ€“2,n > 2 . Find ๐‘Ž_(๐‘›+1)/an, for n = 1,2,3,4,5, Lets first calculate a1 , a2 , a3 , a4 , a5 & a6 It is given that a1 = 1 a2 = 1 For a3 , a4 , a5 & a6 we need to use an = anโ€“1 + anโ€“2 , n > 2 an = an-1 + an-2 , n > 2 Putting n = 3 in (1) a3 = a3 โ€“ 1 + a3 โ€“ 2 = a2 + a1 = 1 + 1 = 2 Putting n = 4 in (1) a4 = a4 โ€“ 1 + a4 โ€“ 2 a4 = a3 + a2 = 2 + 1 = 3 an = an-1 + an-2 , n > 2 Putting n = 5 in (1) a5 = a5 โ€“ 1 + a5 โ€“ 2 a5 = a4 + a3 = 3 + 2 = 5 Putting n = 6 in (1) a6 = a6 โ€“ 1 + a6 โ€“ 2 a6 = a5 + a4 = 5 + 3 = 8 Now, a1 = 1 , a2 = 1, a3 = 2 , a4 = 3 , a5 = 5 , a6 = 8

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