The Fibonacci sequence is defined by `a_1=1=a_2,\ a_n=a_(n-1)+a_(n-2)` for `n > 2.` Find `(a_(n+1))/(a_n)` for `n=1,2,3,4, 5.`

Explanation

`a_n`=`a-(n−1)`+an−2 for n > 2, a = 1

⇒`a_3`=`a_(3−1)`+`a_(3−
2)`=`a_2`+`a_1`=1+1=2

⇒`a_4`=`a_(4−1)`+`a_(4−2)`=`a_3`+`a_2`=2+1=3

⇒`a5`=`a_(5−1)`+`a_(5−2)`=`a_4`+`a_3`=3+2=5

⇒`a_6`=`a_(6−1)`+`a_(6−2)`=`a_5`+`a_4`=5+3=8

∴ For n = 1

`(an+1)/(an)`=`(a2)/(a1)`=`1/1`=1
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