Introduction
Series is a fundamental topic in SSC CGL Reasoning. It tests your ability to identify patterns in sequences of numbers, letters, or symbols. Mastering series helps in solving questions quickly and accurately.
Number Series
Number series involve a sequence of numbers following a specific pattern. Common patterns include arithmetic progression (constant difference), geometric progression (constant ratio), squares/cubes, alternating patterns, and mixed operations.
Key Points
- Check for constant difference or ratio first.
- Look for squares, cubes, or prime numbers.
- Consider alternating patterns (two series interleaved).
- Differences between consecutive terms may follow a pattern.
Solved Example 1
Question: Find the next term: 2, 6, 12, 20, 30, ?
Solution: 42
Explanation: Differences: 4, 6, 8, 10, ... next difference is 12. So 30+12=42.
Letter Series
Letter series involve sequences of letters following alphabetical order, often with skips or alternating patterns. Positions of letters (A=1, B=2, etc.) are used to find the pattern.
Key Points
- Convert letters to numbers for easier pattern recognition.
- Check for constant or increasing skips.
- Look for alternating forward and backward sequences.
- Sometimes letters are combined with numbers.
Solved Example 1
Question: Find the next term: A, C, F, J, O, ?
Solution: U
Explanation: Positions: 1,3,6,10,15. Differences: 2,3,4,5. Next difference 6, so 15+6=21 => U.
Practice Questions
Q1. Find the missing term: 3, 8, 15, 24, ?, 48
Answer: 35
Explanation: Differences: 5,7,9,11,13. So 24+11=35.
Q2. Find the next term: Z, X, U, Q, ?
Answer: L
Explanation: Positions: 26,24,21,17. Differences: -2,-3,-4. Next difference -5 => 17-5=12 => L.
Q3. Find the next term: 1, 4, 9, 16, 25, ?
Answer: 36
Explanation: Squares of natural numbers: 1^2,2^2,3^2,4^2,5^2,6^2=36.
Common Mistakes
- Assuming a pattern without checking multiple terms; always verify with at least three steps.
- Ignoring alternating patterns; if differences don't work, try splitting into two series.
- For letter series, forgetting to convert letters to numbers; always map A=1, B=2, etc.
Quick Revision
- Number series: check differences, ratios, squares, cubes, primes, and alternating patterns.
- Letter series: convert to numbers, check skips, and consider reverse order.
- Mixed series: combine number and letter patterns; look for operations like +2, -3, etc.