If f(n) = f(n-1) + f(n-2) when n >= 2, f(0) = 0, f(1) = 1 then f(7) = ?

Option c: 13. Solution: We are given the recurrence relation: f(n) = f(n-1) + f(n-2) quad text{for } n >= 2 With initial values: f(0) = 0 f(1) = 1 Let's calculate the terms of this sequence (which is the Fibonacci sequence) up to n = 7: - f(2) = f(1) + f(0) = 1 + 0 = 1 - f(3) = f(2) + f(1) = 1 + 1 = 2 - f(4) = f(3) + f(2) = 2 + 1 = 3 - f(5) = f(4) + f(3) = 3 + 2 = 5 - f(6) = f(5) + f(4) = 5 + 3 = 8 - f(7) = f(6) + f(5) = 8 + 5 = 13 The value of f(7) is 13. This corresponds directly to Option C. Note: The textbook answer key incorrectly lists Option D (None of these) as correct, which is a typographical error. Hence, Option C is the correct answer.

If $f(n) = f(n-1) + f(n-2)$ when $n \ge 2$, $f(0) = 0$, $f(1) = 1$ then $f(7) = ?$

The correct answer is Option c: 13. We are given the recurrence relation: $$f(n) = f(n-1) + f(n-2) \quad \text{for } n \ge 2$$ With initial values: $$f(0) = 0$$ $$f(1) = 1$$ Let's calculate the terms of this sequence (which is the Fibonacci sequence) up to $n = 7$: - $f(2) = f(1) + f(0) = 1 + 0 = 1$ - $f(3) = f(2) + f(1) = 1 + 1 = 2$ - $f(4) = f(3) + f(2) = 2 + 1 = 3$ - $f(5) = f(4) + f(3) = 3 + 2 = 5$ - $f(6) = f(5) + f(4) = 5 + 3 = 8$ - $f(7) = f(6) + f(5) = 8 + 5 = 13$ The value of $f(7)$ is $13$. This corresponds directly to Option C. *Note: The textbook answer key incorrectly lists Option D (None of these) as correct, which is a typographical error.* Hence, **Option C** is the correct answer.

Set, Relations and FunctionsPYQ Nov. 19Question 1962 of 217

All Questions

If $\displaystyle f(n) = f(n-1) + f(n-2)$ when $\displaystyle n \ge 2$ , $\displaystyle f(0) = 0$ , $\displaystyle f(1) = 1$ then $\displaystyle f(7) = ?$

Options

C13

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 13

All Options:

A5
B8
C13
DNone of these

Detailed Solution & Explanation

We are given the recurrence relation:

f(n) = f(n-1) + f(n-2) \quad \text{for } n \ge 2

With initial values:

f(0) = 0

f(1) = 1

Let's calculate the terms of this sequence (which is the Fibonacci sequence) up to

\displaystyle n = 7

:
-

\displaystyle f(2) = f(1) + f(0) = 1 + 0 = 1

\displaystyle f(3) = f(2) + f(1) = 1 + 1 = 2

\displaystyle f(4) = f(3) + f(2) = 2 + 1 = 3

\displaystyle f(5) = f(4) + f(3) = 3 + 2 = 5

\displaystyle f(6) = f(5) + f(4) = 5 + 3 = 8

\displaystyle f(7) = f(6) + f(5) = 8 + 5 = 13

The value of

\displaystyle f(7)

\displaystyle 13

.
This corresponds directly to Option C.
*Note: The textbook answer key incorrectly lists Option D (None of these) as correct, which is a typographical error.*
Hence, **Option C** is the correct answer.

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If f(n)=f(n−1)+f(n−2)\displaystyle f(n) = f(n-1) + f(n-2)f(n)=f(n−1)+f(n−2) when n≥2\displaystyle n \ge 2n≥2, f(0)=0\displaystyle f(0) = 0f(0)=0, f(1)=1\displaystyle f(1) = 1f(1)=1 then f(7)=?\displaystyle f(7) = ?f(7)=?