Section 5.2

Series, Codes, and Relationships

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A significant portion of the UGC NET reasoning curriculum focuses on pattern recognition. Recognizing underlying sequences in numbers and letters, and interpreting genealogical descriptions, requires systematic breakdown.

1. Number Series

Number series problems present a sequence of numbers governed by a specific mathematical rule. The objective is to identify the rule to find a missing number or the next number in the sequence.

💡 Candidate Note

Always calculate the difference between consecutive terms first. If the first differences don't show a pattern, calculate the difference of the differences (second-order difference).

  • Arithmetic Series: A constant difference between consecutive terms. E.g., 2, 5, 8, 11 (Difference is +3).
  • Geometric Series: A constant ratio between terms. E.g., 2, 6, 18, 54 (Multiplier is ×3).
  • Prime Series: A sequence of prime numbers. E.g., 2, 3, 5, 7, 11, 13.
  • Square/Cube Series: Based on \( n^2 \) or \( n^3 \). E.g., 1, 4, 9, 16, 25 (Squares).

Example Problem:

Find the next term: 4, 9, 20, 43, ?

Solution: The pattern is \( (\text{Previous Term} \times 2) + 1 \), then \( + 2 \), then \( + 3 \).
4 × 2 + 1 = 9
9 × 2 + 2 = 20
20 × 2 + 3 = 43
Therefore: 43 × 2 + 4 = 90.

2. Letter Coding and Decoding

Letter coding involves encrypting a word using a specific alphabetic shift or substitution. Memorizing the numerical value of the English alphabet (A=1, B=2 ... Z=26) is highly recommended.

Example Problem:

If 'WATER' is coded as 'YCVGT', how is 'FIRE' coded?

Solution: Observe the shift:
W (+2) = Y
A (+2) = C
T (+2) = V
Applying +2 shift to FIRE: F(+2)=H, I(+2)=K, R(+2)=T, E(+2)=G.
Answer: HKTG.

3. Blood Relationships

Blood relation problems describe a family tree using complex verbiage. The most reliable method to solve these is to draw a family tree diagram.

  • Use a square (\(\square\)) for males and a circle (\(\bigcirc\)) for females.
  • Use horizontal lines (\( - \)) for siblings and double lines (\( = \)) for spouses.
  • Use vertical lines (\( | \)) to represent different generations (parent to child).

Example Problem:

Pointing to a photograph, a man said, "I have no brother or sister but that man's father is my father's son." Whose photograph was it?

Solution: "My father's son" refers to the man himself (since he has no siblings). Therefore, the sentence becomes: "That man's father is ME." The photograph is of his son.

Academic References

  • Madaan, K. V. (2023). UGC NET/SET/JRF General Paper-1: Teaching and Research Aptitude (7th ed.). Pearson India.
  • Thorpe, E. (2018). Test of reasoning for competitive examinations (6th ed.). McGraw Hill Education.