Question

The Fibonacci sequence is defined by

$1=a_1=a_{2}nd{a}_n=a_{n-1}+a_{n-1},n>2$.

Find $\frac{a_{n+1}}{a_n}forn=1,2,3,4,5.$

Answer 1

Given : $1=a_1=a_{2}and{a}_n=a_{n-1}+a_{n-1},n>2$ Find $\frac{a_{n+1}}{a_n}forn=1,2,3,4,5.$
Substituting n = 3 , 4 , 5 , 6 we get
$a_3=a_2+a_1=1+1=2$
$a_4=a_3+a_2=2+1=3$
$a_5=a_4+a_3=3+2=5$
$a_6=a_5+a_4=5+3=8$
To find ;$\frac{a_{n+1}}{a_n},n=1,2,3,4,5$
For $n=1\frac{a_{n+1}}{a_n}=\frac{a_2}{a_1}=\frac{1}{1}=1$
For$n=2,\frac{a_{n+1}}{a_n}=\frac{a_3}{a_2}=\frac{2}{1}=2$