The Fibonacci sequence is defined by1 = a1 = a2 and an = an – 1 + an – 2, n > 2 Find \( \dfrac{a_n+1}{a_n}\), for n = 1, 2, 3, 4, 5 

 

Asked by Abhisek | 2 years ago |  129

1 Answer

Solution :-

1 = a1 = a2

an = an – 1 + an – 2, n > 2

So,

a3 = a2 + a1 = 1 + 1 = 2

a4 = a3 + a2 = 2 + 1 = 3

a5 = a4 + a3 = 3 + 2 = 5

a6 = a5 + a4 = 5 + 3 = 8

Substitute the values of 1 a and 2 a in the expression \( \dfrac{a_n+1}{a_n}\) for n=1

for n = 1, \( \dfrac{a_{1+1}}{a_1}= \dfrac{1}{1}=1\)

For n= 2, \( \dfrac{a_{2+1}}{a_2}= \dfrac{2}{1}=2\)

For n= 3, \( \dfrac{a_{3+1}}{a_3}= \dfrac{3}{2}\)

For n= 4, \( \dfrac{a_{4+1}}{a_4}= \dfrac{5}{3}\)

For n= 5, \( \dfrac{a_{5+1}}{a_5}= \dfrac{8}{5}\)

Answered by Pragya Singh | 2 years ago

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