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The Fibonacci sequence is defined by 1 = a1 = a2 and an = an - 1 + an - 2, n > 2. Find an + 1/an for n = 1, 2, 3, 4, 5
Solution:
Here Fibonacci sequence is defined by 1 = a1 = a2 and an = an - 1 + an - 2,
1 = a1 = a2
an = an - 1 + an - 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, a1 + 1/a1
= a2/a1= 1/1 = 1
For n = 2, a2 + 1/a2
= a3/a2 = 2/1 = 2
For n = 3, a3 + 1/a3
= a4/a3 = 3/2
For n = 4, a4 + 1/a4
= a5/a4 = 5/3
For n = 5, a5 + 1/a5
= a6/a5 = 8/5
NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.1 Question 14
The Fibonacci sequence is defined by 1 = a1 = a2 and an = an - 1 + an - 2, n > 2. Find an + 1/an 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 an + 1/an are 1, 2, 3/2, 5/3, 8/5
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