The Fibonacci sequence is defined by1 = a1 = a2 and an = an – 1 + an – 2, n > 2

1 = a₁ = a₂

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