Question

If $F$ is function such that $F(0)=2,F(1)=3,F(x+2)=2F(x)-F(x+1)$ for $x\ge 0$, then $F(5)$ is equal to

• A. -7
• B. -3
• C. 17
• D. 13

Answer 1

Answer: (D)

We have,
$F(x+2)=2F(x)-F(x+1)$ ... (i)
Putting $x=0$, we get
$F(2)=2F(0)-F(1)$
$\Rightarrow F(2)=2(2)-3$
$\{\because F(0)=2,F(1)=3\}$
$\Rightarrow F(2)=4-3$
$\Rightarrow F(2)=1$
Putting $x=1$, in Eq. (i), we get
$F(3)=2F(1)-F(2)$
$=2(3)-1\{\because F(1)=3,F(2)=1\}$
$\Rightarrow F(3)=5$
Putting $x=2$, in Eq. (i), we get
$F(4)=2F(2)-F(3)$
$=2(1)-5\{\because F(2)=1,F(3)=5\}$
$F(4)=-3$
Putting $x=3$, in Eq. (i), we get
$F(5)=2F(3)-F(4)$
$=2(5)+3\{\because F(3)=5,F(4)=-3\}$
$\Rightarrow F(5)=13$