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Read the instructions below and solve.
f(x) = f(x – 2) – f(x – 1), x is a natural number
f(1) = 0, f(2) = 1
f(x) = f(x – 2) – f(x – 1), x is a natural number
f(1) = 0, f(2) = 1
The value of f(8) is
- a)0
- b)13
- c)–5
- d)–9
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Read the instructions below and solve.f(x) = f(x – 2) – f(...
f(1) = 0, f(2) = 1,
f(3) = f(1) – f(2) = –1
f(4) = f(2) – f(3) = 2
f(5) = f(3) – f(4) = –3
f(6) = f(4) – f(5) = 5
f(7) = f(5) – f(6) = –8
f(8) = f(6) – f(7) = 13
f(9) = f(7) – f(8) = –21
f(3) = f(1) – f(2) = –1
f(4) = f(2) – f(3) = 2
f(5) = f(3) – f(4) = –3
f(6) = f(4) – f(5) = 5
f(7) = f(5) – f(6) = –8
f(8) = f(6) – f(7) = 13
f(9) = f(7) – f(8) = –21
13
Most Upvoted Answer
Read the instructions below and solve.f(x) = f(x – 2) – f(...
Given information:
- f(x) = f(x-2) + f(x-1)
- f(1) = 0
- f(2) = 1
To find:
- The value of f(8)
Approach:
- We can solve this problem using a recursive approach.
- We will start by finding the values of f(3), f(4), f(5), f(6), f(7), and finally f(8) based on the given information and the given equation.
Solution:
Step 1: Find the value of f(3)
- We know that f(3) = f(3-2) + f(3-1)
- f(3) = f(1) + f(2) [Using the given equation]
- f(3) = 0 + 1 [Using the given values]
- f(3) = 1
Step 2: Find the value of f(4)
- We know that f(4) = f(4-2) + f(4-1)
- f(4) = f(2) + f(3) [Using the given equation]
- f(4) = 1 + 1 [Using the given values]
- f(4) = 2
Step 3: Find the value of f(5)
- We know that f(5) = f(5-2) + f(5-1)
- f(5) = f(3) + f(4) [Using the given equation]
- f(5) = 1 + 2 [Using the values we found in Step 1 and Step 2]
- f(5) = 3
Step 4: Find the value of f(6)
- We know that f(6) = f(6-2) + f(6-1)
- f(6) = f(4) + f(5) [Using the given equation]
- f(6) = 2 + 3 [Using the values we found in Step 2 and Step 3]
- f(6) = 5
Step 5: Find the value of f(7)
- We know that f(7) = f(7-2) + f(7-1)
- f(7) = f(5) + f(6) [Using the given equation]
- f(7) = 3 + 5 [Using the values we found in Step 3 and Step 4]
- f(7) = 8
Step 6: Find the value of f(8)
- We know that f(8) = f(8-2) + f(8-1)
- f(8) = f(6) + f(7) [Using the given equation]
- f(8) = 5 + 8 [Using the values we found in Step 4 and Step 5]
- f(8) = 13
Conclusion:
- The value of f(8) is 13 (Option B).
- f(x) = f(x-2) + f(x-1)
- f(1) = 0
- f(2) = 1
To find:
- The value of f(8)
Approach:
- We can solve this problem using a recursive approach.
- We will start by finding the values of f(3), f(4), f(5), f(6), f(7), and finally f(8) based on the given information and the given equation.
Solution:
Step 1: Find the value of f(3)
- We know that f(3) = f(3-2) + f(3-1)
- f(3) = f(1) + f(2) [Using the given equation]
- f(3) = 0 + 1 [Using the given values]
- f(3) = 1
Step 2: Find the value of f(4)
- We know that f(4) = f(4-2) + f(4-1)
- f(4) = f(2) + f(3) [Using the given equation]
- f(4) = 1 + 1 [Using the given values]
- f(4) = 2
Step 3: Find the value of f(5)
- We know that f(5) = f(5-2) + f(5-1)
- f(5) = f(3) + f(4) [Using the given equation]
- f(5) = 1 + 2 [Using the values we found in Step 1 and Step 2]
- f(5) = 3
Step 4: Find the value of f(6)
- We know that f(6) = f(6-2) + f(6-1)
- f(6) = f(4) + f(5) [Using the given equation]
- f(6) = 2 + 3 [Using the values we found in Step 2 and Step 3]
- f(6) = 5
Step 5: Find the value of f(7)
- We know that f(7) = f(7-2) + f(7-1)
- f(7) = f(5) + f(6) [Using the given equation]
- f(7) = 3 + 5 [Using the values we found in Step 3 and Step 4]
- f(7) = 8
Step 6: Find the value of f(8)
- We know that f(8) = f(8-2) + f(8-1)
- f(8) = f(6) + f(7) [Using the given equation]
- f(8) = 5 + 8 [Using the values we found in Step 4 and Step 5]
- f(8) = 13
Conclusion:
- The value of f(8) is 13 (Option B).
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Read the instructions below and solve.f(x) = f(x – 2) – f(x – 1), x is a natural numberf(1) = 0, f(2) = 1The value of f(8) isa)0b)13c)–5d)–9Correct answer is option 'B'. Can you explain this answer?
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Read the instructions below and solve.f(x) = f(x – 2) – f(x – 1), x is a natural numberf(1) = 0, f(2) = 1The value of f(8) isa)0b)13c)–5d)–9Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Read the instructions below and solve.f(x) = f(x – 2) – f(x – 1), x is a natural numberf(1) = 0, f(2) = 1The value of f(8) isa)0b)13c)–5d)–9Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the instructions below and solve.f(x) = f(x – 2) – f(x – 1), x is a natural numberf(1) = 0, f(2) = 1The value of f(8) isa)0b)13c)–5d)–9Correct answer is option 'B'. Can you explain this answer?.
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