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Fibonacci-like

Fibonacci-like sequences are defined by the recurrence relation where each term is the sum of the two preceding terms. The classic Fibonacci sequence starts with 0,1,1,2,3,5,8,13... Variations may use different starting numbers. These problems test your ability to apply recursive addition patterns.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Fibonacci-like

Fibonacci-like sequences are defined by the recurrence relation where each term is the sum of the two preceding terms. The classic Fibonacci sequence starts with 0,1,1,2,3,5,8,13... Variations may use different starting numbers. These problems test your ability to apply recursive addition patterns.

Prerequisites

Basic addition Understanding of recursive patterns Two-term dependence Pattern extension skills
Why This Matters: Fibonacci-like problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test recursive pattern recognition.

How to Solve Fibonacci-like Problems

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Step 1: Identify the first two terms of the sequence

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Step 2: Each subsequent term is the sum of the two preceding terms

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Step 3: Verify the pattern for at least two steps

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Step 4: For next term: add the last two terms

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Step 5: For missing term: use the sum relationship

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Step 6: For wrong term identification: check if term equals sum of previous two

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Step 7: Verify your answer by working backwards

Pro Strategy: Always verify that each term (after the first two) equals the sum of the two terms before it. This pattern must hold consistently throughout the sequence.

Example Problem

Example: Find the next term in the sequence: 2, 3, 5, 8, 13, ___ Solution: Step 1: First two terms: 2 and 3 Step 2: 2+3=5, 3+5=8, 5+8=13 Step 3: Pattern holds: each term = sum of previous two Step 4: Next term = 8 + 13 = 21 Answer: 21

Pro Tips & Tricks

  • Classic Fibonacci: 0,1,1,2,3,5,8,13,21,34...
  • Lucas numbers: 2,1,3,4,7,11,18,29...
  • Each term after the second is the sum of the two preceding terms
  • The ratio of consecutive terms approaches the golden ratio φ ≈ 1.618
  • To find a term, you need both preceding terms
  • Tribonacci sequences use sum of three previous terms

Shortcut Methods to Solve Faster

Next term = Last term + Second last term
Previous term = Current term - Previous term
The sequence grows exponentially over time

Common Mistakes to Avoid

Adding only one previous term instead of two
Starting with incorrect initial terms
Confusing with geometric progression
Not verifying the pattern for multiple steps

Exam Importance

Fibonacci-like is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
1-2 questions
INSURANCE
1-2 questions

Ready to Master Fibonacci-like?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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