Question

$Considerthefollowingstatements:$

$F_{00}\left(0\right)-1,F_{00}\left(1\right)=1$

$F_{00}\left(n\right)=10\times F_{00}(n-1)+100\times F_{00}(n-2)forn\ge 2$

$Thenwhatwillbethevalueof{F}_{00}\left(3\right)?$

• A. $1200$
• B. $1$
• C. $600$
• D. $110$

Answer 1

The correct option is A $1200$

$F_{00}\left(0\right)=1,F_{00}\left(1\right)=1$

$F_{00}\left(n\right)=10\times F_{00}(n-1)+100F_{00}(n-2),ifn\ge 2$

$F_{00}\left(2\right)=10\times F_{00}\left(1\right)+100F_{00}\left(0\right)$

$=(10\times 1)+(100\times 1)$

$=10+100$

$=110$


$Similarly:$

$F_{00}\left(3\right)=10\times F_{00}\left(2\right)+100F_{00}\left(1\right)$

$=(10\times 110)+(100\times 1)$

$=1100+100$

$=1200$