Question

F1=1,F2=3 and Fn=Fn-1+Fn-2 then F5 is​

Answer 1

GIVEN :

$F_1=1$, $F_2=3$ and $F_n=F_{n-1}+F_{n-2}$

TO FIND :

The value of $F_5$

SOLUTION :

Given that the values are $F_1=1$, $F_2=3$ and $F_n=F_{n-1}+F_{n-2}$

Now put n = 3  in $F_n=F_{n-1}+F_{n-2}$ we get

$F_3=F_{3-1}+F_{3-2}$

⇒ $F_3 = F_2 + F_1$

$F_3=3+1$

∴ $F_3=4$

Now put n = 4  in $F_n=F_{n-1}+F_{n-2}$ we get

$F_4=F_{4-1}+F_{4-2}$

⇒ $F_4 = F_3 + F_2$

$F_4=4+3$

∴ $F_4=7$

 Now put n = 5  in $F_n=F_{n-1}+F_{n-2}$ we get

$F_5=F_{5-1}+F_{5-2}$

⇒ $F_5 = F_4 + F_3$

$F_5=7+4$

∴ $F_5=11$

The value of $F_5$ is 11