The Fibonacci sequence is defined by 1 = a₁ = a₂ and a_n = a_{n - 1} + a_{n - 2}, n > 2. Find a_{n + 1}/a_n for n = 1, 2, 3, 4, 5

Solution:

Here Fibonacci sequence is defined by 1 = a₁ = a₂ and a_n = a_{n - 1} + a_{n - 2},

1 = a₁ = a₂

a_n = a_{n - 1} + a_{n - 2}, n > 2

Therefore,

a₃ = a₂ + a₁ = 1 + 1 = 2

a₄ = a₃ + a₂ = 2 + 1 = 3

a₅ = a₄ + a₃ = 3 + 2 = 5

a₆ = a₅ + a₄ = 5 + 3 = 8

For n = 1, a_{1 + 1}/a₁

= a₂/a₁= 1/1 = 1

For n = 2, a_{2 + 1}/a₂

= a₃/a₂ = 2/1 = 2

For n = 3, a_{3 + 1}/a₃

= a₄/a₃ = 3/2

For n = 4, a_{4 + 1}/a₄

= a₅/a₄ = 5/3

For n = 5, a_{5 + 1}/a₅

= a₆/a₅ = 8/5

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.1 Question 14

The Fibonacci sequence is defined by 1 = a₁ = a₂ and a_n = a_{n - 1} + a_{n - 2}, n > 2. Find a_{n + 1}/a_n for n = 1, 2, 3, 4, 5

Summary:

We are given the formula for the Fibonacci sequence above. Using this the first terms for the sequence a_{n + 1}/a_n are 1, 2, 3/2, 5/3, 8/5