Finding Sequences

Chapter 9 Class 11 Sequences and Series
Concept wise

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Ex9.1 , 14 The Fibonacci sequence is defined by 1 = a1 = a2 and an = anβ1+anβ2,n > 2 . Find π_(π+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 = anβ1 + anβ2 , n > 2 an = an-1 + an-2 , n > 2 Putting n = 3 in (1) a3 = a3 β 1 + a3 β 2 = a2 + a1 = 1 + 1 = 2 Putting n = 4 in (1) a4 = a4 β 1 + a4 β 2 a4 = a3 + a2 = 2 + 1 = 3 an = an-1 + an-2 , n > 2 Putting n = 5 in (1) a5 = a5 β 1 + a5 β 2 a5 = a4 + a3 = 3 + 2 = 5 Putting n = 6 in (1) a6 = a6 β 1 + a6 β 2 a6 = a5 + a4 = 5 + 3 = 8 Now, a1 = 1 , a2 = 1, a3 = 2 , a4 = 3 , a5 = 5 , a6 = 8

Davneet Singh

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