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Alternating Series

Alternating Series problems use two different operations that alternate between terms. Common patterns include: add then multiply, add then subtract, multiply then add, or alternating between two different constants. These problems test your ability to recognize and handle mixed 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 Alternating Series

Alternating Series problems use two different operations that alternate between terms. Common patterns include: add then multiply, add then subtract, multiply then add, or alternating between two different constants. These problems test your ability to recognize and handle mixed patterns.

Prerequisites

Basic arithmetic operations Pattern recognition Understanding of alternating patterns Two-step pattern analysis
Why This Matters: Alternating Series problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test recognition of mixed patterns.

How to Solve Alternating Series Problems

1

Step 1: Calculate the differences or ratios between consecutive terms

2

Step 2: Look for a repeating pattern of two different operations

3

Step 3: Common patterns: +a, ×b, +a, ×b,... or ×a, +b, ×a, +b,...

4

Step 4: Identify the two operations and their values

5

Step 5: Apply the appropriate operation based on position parity

6

Step 6: For the next term, apply the next operation in the cycle

7

Step 7: Verify the pattern holds for all given terms

Pro Strategy: Alternating patterns often involve two different operations that repeat in a cycle. Identify the pattern by looking at pairs of terms. The operation type may depend on whether the position is odd or even.

Example Problem

Example: Find the next term: 2, 5, 10, 13, 26, 29, ___ Solution: Step 1: Differences: +3, +5, +3, +13, +3 (not consistent) Step 2: Pattern: +3, ×2, +3, ×2, +3,... Step 3: Next operation after +3 is ×2 Step 4: 29 × 2 = 58 Answer: 58

Pro Tips & Tricks

  • Common pattern: +a, ×b, +a, ×b,...
  • Another pattern: ×a, +b, ×a, +b,...
  • Separate odd and even position terms into two sequences
  • Check if the sequence interleaves two different progressions
  • The operations may change between addition, subtraction, multiplication, division
  • Pattern length could be 2, 3, or more operations in cycle

Shortcut Methods to Solve Faster

If pattern alternates between two operations, apply the next operation in sequence
Odd positions may follow one rule, even positions another
The cycle length is the number of operations before repetition
Test the pattern on three consecutive operations to confirm

Common Mistakes to Avoid

Assuming a single operation when pattern alternates
Mixing up which operation applies to which term
Not verifying the pattern for multiple cycles
Confusing alternating operations with interleaved sequences

Exam Importance

Alternating 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 Alternating 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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