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Multiplication Series

Multiplication Series problems involve sequences where each term is generated by multiplying the previous term by a constant and then adding (or subtracting) another constant. Common patterns include ×k + c, ×k - c, or ×k + c with varying operations.

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 Multiplication Series

Multiplication Series problems involve sequences where each term is generated by multiplying the previous term by a constant and then adding (or subtracting) another constant. Common patterns include ×k + c, ×k - c, or ×k + c with varying operations.

Prerequisites

Multiplication and addition skills Pattern recognition Linear recurrence understanding Compound operation analysis
Why This Matters: Multiplication Series problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test understanding of compound operations.

How to Solve Multiplication Series Problems

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Step 1: Calculate the operation between the first two terms

2

Step 2: Test if the same operation applies to subsequent pairs

3

Step 3: Common pattern: aₙ = aₙ₋₁ × k + c

4

Step 4: Solve for k and c using two equations if needed

5

Step 5: Apply the pattern to find the next term

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Step 6: Verify the pattern holds for all given terms

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

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

Multiplication Series 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
GMAT
1-2 questions
INSURANCE
1-2 questions

Ready to Master Multiplication Series?

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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