Q. If a function $F$ is such that $F(0) = 2,\ F(1) = 3,\ F(n + 2) = 2F(n) - F(n + 1)$ for $n \neq 0$, then $F(5)$ is equal to
A) -7
B) -3
C) 7
D) 13
Explanation
(d)
Given, $F(0) = 2,\ \ \ \ F(1) = 3,$
Since, $F(n + 2) = 2F(n) - F(n + 1)$
At $n = 0,\ \ \ \ \ F(0 + 2) = 2F(0) - F(1)$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ F(2) = 2(2) - 3 = 1$
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 $n = 3,\ \ \ \ F(3 + 2) = 2F(3) - F(4) = 2(5) - ( - 3)$
$\Rightarrow \ \ \ F(5) = 13$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.