The Fibonacci sequence is defined by 1- a 1 - a 2 -2- a n - a n-1 - a n-2 -n-2- Find an-1an- for n-1-2-3-4-5

We have, a_n=a_n 1+a_n 2 and #160;1= a _ 1 = a _ 2 a _ n = a _ n 1 + a _ n 2 ,n gt;2 ∴ a _ 3 = a _ 2 + a _ 1 =1+1=2 a _ 4 = a _ 3 + a ...

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Standard VII

Mathematics

Division of Fractions

The Fibonacci...

Question

The Fibonacci sequence is defined by $1 = a_{1} = a_{2} = 2, a_{n} = a_{n - 1} + a_{n - 2}, n > 2.$ Find $\frac{a_{n + 1}}{a_{n}},$ for $n = 1, 2, 3, 4, 5$

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Solution

We have, $a_{n} = a_{n - 1} + a_{n - 2}$
and $1 = a_{1} = a_{2} a_{n} = a_{n - 1} + a_{n - 2}, n > 2 ∴ a_{3} = a_{2} + a_{1} = 1 + 1 = 2 a_{4} = a_{3} + a_{2} = 2 + 1 = 3 a_{5} = a_{4} + a_{3} = 3 + 2 = 5 a_{6} = a_{5} + a_{4} = 5 + 3 = 8$

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

We have, an=an−1+an−2and 1=a1=a2an=an−1+an−2,n>2∴a3=a2+a1=1+1=2a4=a3+a2=2+1=3a5=a4+a3=3+2=5a6=a5+a4=5+3=8

The Fibonacci sequence is defined by $1 = a_{1} = a_{2} = 2, a_{n} = a_{n - 1} + a_{n - 2}, n > 2.$ Find $\frac{a_{n + 1}}{a_{n}},$ for $n = 1, 2, 3, 4, 5$

We have, $a_{n} = a_{n - 1} + a_{n - 2}$
and $1 = a_{1} = a_{2} a_{n} = a_{n - 1} + a_{n - 2}, n > 2 ∴ a_{3} = a_{2} + a_{1} = 1 + 1 = 2 a_{4} = a_{3} + a_{2} = 2 + 1 = 3 a_{5} = a_{4} + a_{3} = 3 + 2 = 5 a_{6} = a_{5} + a_{4} = 5 + 3 = 8$