Question

If a function F is such that $f(0)=2,F(1)=3,$ $F(n+2)=2F(n)-F(n+1)$ for $n\ne 0,$ then $F(5)$ is equal to

• A. $-7$
• B. $-3$
• C. $7$
• D. $13$

Answer 1

Answer: (D)

Given that, $F(0)=2,F(1)=3,$ $F(n+2)=2F(n)-F(n+1)$ At $n=0,F(0+2)=2F(0)-F(1)$
$\Rightarrow$ $F(3)=2(2)-3=1$ At $n=1,F(1+2)=2F(1)-F(2)$
$\Rightarrow$ $F(3)=2(3)-1=5$ At $n=2,F(2+2)=2F(2)-F(3)$
$\Rightarrow$ $F(4)=2(1)-5=-3$ At $n=3,F(3+2)=2F(3)-F(4)$
$=2(5)-(-3)$
$\Rightarrow$ $F(5)=13$