Question

Ankita has to climb 5 stairs starting at the ground, while respecting the following rules: 1. At any stage, Ankita can move either one or two stairs up. 2. At any stage, Ankita cannot move to a lower step. Let $F(N)$ denote the number of possible ways in which Ankita can reach the $N^{th}$ stair. For example, $F(1) = 1$, $F(2) = 2$, $F(3) = 3$. The value of $F(5)$ is .................

• A. 8
• B. 7
• C. 6
• D. 5

Hint:

This is a classical example of the Fibonacci-like sequence, where each number is the sum of the two preceding ones.

Answer 1

The Correct Option is A

We are given the recurrence relation that $F(1) = 1$, $F(2) = 2$, and $F(3) = 3$. The number of ways to reach any stair $N$ depends on whether Ankita took one or two steps from the previous stair: \[ F(N) = F(N-1) + F(N-2) \] Now, let us calculate $F(4)$ and $F(5)$: \[ F(4) = F(3) + F(2) = 3 + 2 = 5 \] \[ F(5) = F(4) + F(3) = 5 + 3 = 8 \] Therefore, the value of $F(5) = 8$.