Series Completion — SOF NSO Study Notes

Overview

Series completion is a core logical reasoning topic that appears in almost every SOF NSO paper. It tests your ability to recognize patterns, predict the next element, and identify relationships between consecutive terms. In the exam, you will encounter three main types of series: number series (numerical progression), alphabet series (letter patterns) and figural series (shape/pattern sequences).

Mastering series completion requires practice in spotting common operations like addition, subtraction, multiplication, squaring, prime numbers, and alternating patterns. For alphabet series, you must be comfortable with letter positions (A=1, B=2...Z=26) and pattern jumps. Figural series demand visual pattern recognition—rotation, reflection, element addition/removal.

Expect 4–6 questions on series completion in the reasoning section. These are high-scoring questions if you develop systematic observation skills. Always look for the simplest pattern first, then check if it holds for all given terms before selecting your answer.

Key Concepts

• **Pattern Recognition**: Every series follows a rule or operation applied consistently across terms. Your job is to decode this rule by examining differences, ratios or transformations between consecutive elements.

• **Number Series Operations**: Common patterns include arithmetic progression (constant addition/subtraction), geometric progression (constant multiplication/division), squares/cubes, prime numbers, Fibonacci-style addition (sum of previous two terms), and alternating operations.

• **Alphabet Series Logic**: Letters are treated as numbers based on position. Patterns include fixed jumps (+2, +3, etc.), reverse alphabets, skipping letters, or alternating forward/backward movements. Remember Z wraps to A in cyclic patterns.

• **Mixed Series**: Some series alternate between two sub-patterns. Example: odd positions follow one rule, even positions follow another. Always separate the series into sub-sequences when simple patterns don't fit.

• **Figural Series**: Visual patterns involve rotation (clockwise/anticlockwise), reflection (horizontal/vertical flip), addition/removal of elements, shading changes, or size progression. Count elements systematically.

• **Wrong Term Identification**: Sometimes you're given a series with one wrong element. Apply the pattern rule to each position and spot which term breaks it.

• **Missing Middle Term**: The blank can appear anywhere in the series, not just at the end. Establish the pattern using complete terms, then apply it to find the missing one.

• **Multiple Operations**: Complex series may combine two operations alternately. Example: +3, ×2, +3, ×2... Always test your discovered pattern on all visible transitions.

Formulas / Key Facts

• **Alphabet Positions**: A=1, B=2, C=3...Z=26. Reverse: Z=1, Y=2...A=26.
• **Square Numbers**: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225...
• **Cube Numbers**: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000...
• **Prime Numbers**: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47...
• **Fibonacci Pattern**: Each term = sum of previous two terms (1, 1, 2, 3, 5, 8, 13, 21...)
• **Arithmetic Progression (AP)**: Next term = Previous term + constant difference.
• **Geometric Progression (GP)**: Next term = Previous term × constant ratio.
• **Alternating Series Formula**: Check if positions 1,3,5,... follow one rule and 2,4,6,... follow another.

Worked Examples

**Example 1: Number Series** Find the next term: 3, 7, 15, 31, 63, ?

*Solution*: Examine differences: 7-3=4, 15-7=8, 31-15=16, 63-31=32. The differences are doubling (4, 8, 16, 32). Next difference should be 64. Therefore, next term = 63 + 64 = **127**.

Alternative pattern check: Each term is (2^n - 1) where n=2,3,4,5,6,7. So 2^7-1=128-1=127 ✓

**Example 2: Alphabet Series** Find the missing term: B, E, I, N, T, ?

*Solution*: Convert to positions: B=2, E=5, I=9, N=14, T=20. Check differences: 5-2=3, 9-5=4, 14-9=5, 20-14=6. The gap increases by 1 each time. Next gap = 7. So 20+7=27, but we only have 26 letters. 27-26=1, so it cycles to position 1 = **A**.

**Example 3: Mixed Alternating Series** Find the next term: 2, 5, 6, 10, 18, 20, ?

*Solution*: Separate odd and even positions. Odd positions (1st, 3rd, 5th, 7th): 2, 6, 18, ?. Pattern: 2×3=6, 6×3=18, so 18×3=54. Even positions (2nd, 4th, 6th): 5, 10, 20. Pattern: 5×2=10, 10×2=20. Since we need the 7th term (odd position), answer is **54**.

**Example 4: Figural Series** Series shows: Square with 1 dot → Triangle with 2 dots → Circle with 3 dots → Square with 4 dots → ?

*Solution*: Two patterns running together. Shape sequence: Square, Triangle, Circle (repeats). So next is Triangle. Dot count: increases by 1 each time (1,2,3,4...). Next should have 5 dots. Answer: **Triangle with 5 dots**.

Common Mistakes

• **Assuming Linear Patterns Only**: Students often look only for constant addition and miss multiplication, squaring or mixed patterns. → Always check differences first, then ratios, then squares/cubes if simple patterns fail.

• **Ignoring Alternating Sub-patterns**: When a pattern doesn't make sense, students force a single rule. → Split the series into odd and even positions and analyze separately.

• **Alphabet Wraparound Errors**: Forgetting that Z+1 = A causes wrong answers in cyclic alphabet series. → When position exceeds 26, subtract 26 to cycle back.

• **Overlooking Direction in Figural Series**: Missing whether shapes rotate clockwise or anticlockwise, or flip horizontally vs vertically. → Mark reference points on complex figures and track their exact movement.

• **Not Verifying the Pattern**: Jumping to an answer after checking only two terms. → Always verify your discovered rule works for ALL given transitions before applying to the missing term.

Quick Reference

• Check differences between consecutive terms first, then second-order differences if needed.
• For alphabet series, convert letters to numbers (A=1...Z=26) and find the numerical pattern.
• Separate alternating series into two sub-sequences when no single pattern fits.
• Common number patterns: +n, ×n, n², n³, primes, Fibonacci, alternating add/multiply.
• In figural series, count elements, track rotation direction and note shading changes systematically.
• Always test your pattern on all visible terms before selecting the answer.