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# The Fibonacci sequence is defined by 1 = a_{1} = a_{2} 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 = a_{1} = a_{2} and a_{n} = a_{n - 1} + a_{n - 2},

1 = a_{1} = a_{2}

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

Therefore,

a_{3} = a_{2} + a_{1} = 1 + 1 = 2

a_{4} = a_{3} + a_{2} = 2 + 1 = 3

a_{5} = a_{4} + a_{3} = 3 + 2 = 5

a_{6} = a_{5} + a_{4} = 5 + 3 = 8

For n = 1, a_{1}_{ + 1}/a_{1 }

= a_{2}/a_{1}= 1/1 = 1

For n = 2, a_{2 + 1}/a_{2 }

= a_{3}/a_{2 }= 2/1 = 2

For n = 3, a_{3 + 1}/a_{3 }

= a_{4}/a_{3 }= 3/2

For n = 4, a_{4 + 1}/a_{4}

= a_{5}/a_{4 }= 5/3

For n = 5, a_{5 + 1}/a_{5}

= a_{6}/a_{5} = 8/5

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.1 Question 14

## The Fibonacci sequence is defined by 1 = a_{1} = a_{2} 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

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