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The Fibonacci sequence is defined by 1=...

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.

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According to the question `a_1=a_2=1 ` and `a_n=a_(n-1)+a_(n-2)`
Substituting `n=3,4,5,6 `
`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`
Now `a_(n+1)/a_n` for `n=1,2,3,4,5 `
For `n=1` , `a_2/a_1=1/1=1`
`n=2 ` , `a_3/a_2=2/1=2`
`n=3` , `a_4/a_3=3/2`
`n=4` , `a_5/a_4=5/3`
`n=5`, `a_6/a_5=8/5`
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