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Mixed Operations

Mixed Operations sequences involve applying a sequence of different arithmetic operations to each term to get the next. Common patterns include: ×2, +3, ×2, +3,... or +4, ×2, -1, +4, ×2, -1,... These problems test your ability to recognize and apply multi-step operation patterns.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 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 Mixed Operations

Mixed Operations sequences involve applying a sequence of different arithmetic operations to each term to get the next. Common patterns include: ×2, +3, ×2, +3,... or +4, ×2, -1, +4, ×2, -1,... These problems test your ability to recognize and apply multi-step operation patterns.

Prerequisites

All basic arithmetic operations Pattern recognition Order of operations Multi-step pattern analysis
Why This Matters: Mixed Operations problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test complex pattern recognition.

How to Solve Mixed Operations Problems

1

Step 1: Calculate the operation between the first two terms

2

Step 2: Calculate the operation between the second and third terms

3

Step 3: Identify the sequence of operations (may repeat cyclically)

4

Step 4: Determine the operation pattern length

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Step 5: Apply the next operation to the last term

6

Step 6: Verify the pattern holds for all given terms

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Step 7: Present the next term

Pro Strategy: Look for patterns like multiply then add, add then multiply, or chains of operations. The operations may be constant or may alternate. Write each step as an operation on the previous term.

Example Problem

Example: Find the next term: 3, 7, 15, 31, 63, ___ Solution: Step 1: 3→7 (×2+1), 7→15 (×2+1), 15→31 (×2+1), 31→63 (×2+1) Step 2: Pattern: multiply by 2 and add 1 Step 3: Next term = 63 × 2 + 1 = 127 Answer: 127

Pro Tips & Tricks

  • Common pattern: aₙ = aₙ₋₁ × k + c
  • Pattern can be: +a, ×b, -c, then repeat
  • Write terms as: term₂ = f(term₁), term₃ = f(term₂), etc.
  • The function f may be the same for all steps or may vary cyclically
  • Check if operations are applied in a fixed cycle (length 2,3,4)
  • Sometimes the operation depends on term position (odd/even)

Shortcut Methods to Solve Faster

If pattern is aₙ = aₙ₋₁ × k + c, find k and c from two equations
For alternating operations, separate odd/even positions
Check if sequence fits polynomial pattern
Try: aₙ = aₙ₋₁ × 2, then aₙ = aₙ₋₁ + 1, etc.

Common Mistakes to Avoid

Assuming a single operation when multiple are used
Not identifying the cycle length correctly
Applying operations in wrong order
Missing that operations may change between steps

Exam Importance

Mixed Operations 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 Mixed Operations?

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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