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Alternating Series

Alternating Series problems involve sequences where two different patterns alternate positions. For example, odd positions might follow one arithmetic progression while even positions follow another. These problems test your ability to identify and separate multiple interleaved 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 involve sequences where two different patterns alternate positions. For example, odd positions might follow one arithmetic progression while even positions follow another. These problems test your ability to identify and separate multiple interleaved patterns.

Prerequisites

Alphabet positions Arithmetic series concepts Pattern recognition Ability to separate interleaved sequences
Why This Matters: Alternating Series problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test advanced pattern recognition skills.

How to Solve Alternating Series Problems

1

Step 1: Write down the positions of all given letters

2

Step 2: Separate odd-position terms (1st, 3rd, 5th...) into one sequence

3

Step 3: Separate even-position terms (2nd, 4th, 6th...) into another sequence

4

Step 4: Find the pattern/difference in each separate sequence

5

Step 5: Determine which position the next term occupies

6

Step 6: Apply the appropriate pattern to find the next term's position

7

Step 7: Convert the position back to a letter

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Step 8: Verify both patterns are consistent

Pro Strategy: Always separate the series into two or more interleaved sequences. Analyze each sub-sequence independently. The pattern in each sub-sequence is usually simple arithmetic progression.

Example Problem

Example: Find the next letter: A, C, B, E, C, G, D, ___ Solution: Step 1: Positions: A=1, C=3, B=2, E=5, C=3, G=7, D=4 Step 2: Odd positions (1st,3rd,5th,7th): 1, 2, 3, 4 → +1 each time Step 3: Even positions (2nd,4th,6th): 3, 5, 7 → +2 each time Step 4: Next is 8th term (even position) Step 5: Next even term = 7 + 2 = 9 Step 6: Position 9 = I Answer: I Example 2: Find the next letter: B, E, D, G, F, I, H, ___ Solution: Step 1: Odd positions (1st,3rd,5th,7th): B=2, D=4, F=6, H=8 → +2 each Step 2: Even positions (2nd,4th,6th): E=5, G=7, I=9 → +2 each Step 3: Next (8th term, even) = 9 + 2 = 11 = K Answer: K

Pro Tips & Tricks

  • Write terms with their position numbers (1st, 2nd, 3rd...) for clarity
  • Use different colors or highlighting to separate odd/even positions
  • Common alternating patterns: +1,+2,+1,+2 or +2,+3,+2,+3
  • Sometimes three patterns interleave (positions 1,4,7... etc.)
  • Check if each sub-sequence follows a simple arithmetic progression
  • The step size in each sub-sequence may be different

Shortcut Methods to Solve Faster

For two alternating patterns: odd positions follow pattern P1, even positions follow P2
The next term's pattern is determined by its position parity
If positions follow AP, the sub-sequences also follow AP with step = original step × 2

Common Mistakes to Avoid

Trying to find a single pattern for the entire sequence
Misidentifying which terms belong to which sub-sequence
Not checking both patterns for consistency
Forgetting to convert positions back to letters

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

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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