4.4 Number and Letter Series

Number and Letter Series

Series questions test pattern recognition under time pressure. You are given a sequence of numbers or letters with one term missing (usually the last one) and must determine the rule that generates the sequence, then apply that rule to find the missing term. This section covers the four most common number-series patterns and two common letter-series patterns, with worked examples for each.

General Strategy

1. Find the difference between each consecutive pair of terms. If the differences are constant, it's an arithmetic series.
2. If the differences are not constant, check the ratio between consecutive terms (divide each term by the one before it). If the ratio is constant, it's a geometric (multiplicative) series.
3. If neither works, check whether the series alternates between two different rules applied to alternating terms.
4. If none of those work, look at the differences of the differences (second-level differences) — many series are built from a changing gap.
5. For letters, convert each letter to its alphabet position (A=1, B=2, C=3 ... Z=26) and apply the same numeric strategies.

Alphabet Position Reference

Keep a copy of this table in the margin of your scratch paper throughout the exam — under time pressure, mentally counting from A is slower and more error-prone than reading a position directly off a written table.

Pattern 1: Arithmetic Progression (Constant Difference)

Worked Example: 7, 12, 17, 22, ___

• Step 1: Find the differences: 12 − 7 = 5, 17 − 12 = 5, 22 − 17 = 5. The difference is constant at +5.
• Step 2: Apply the rule to the last term: 22 + 5 = 27.

Answer: 27.

Pattern 2: Geometric / Multiplicative Progression (Constant Ratio)

Worked Example: 2, 6, 18, 54, ___

• Step 1: Check the differences first: 4, 12, 36 — not constant, so it is not arithmetic.
• Step 2: Check the ratio: 6 ÷ 2 = 3, 18 ÷ 6 = 3, 54 ÷ 18 = 3. The ratio is constant at ×3.
• Step 3: Apply the rule: 54 × 3 = 162.

Answer: 162.

Pattern 3: Alternating Two-Pattern Series

Some series apply two different operations that alternate back and forth.

Worked Example: 5, 10, 8, 16, 14, 28, ___

• Step 1: Look at the operation from each term to the next: 5 → 10 (×2), 10 → 8 (−2), 8 → 16 (×2), 16 → 14 (−2), 14 → 28 (×2).
• Step 2: The pattern alternates ×2, −2, ×2, −2, ×2, .... The next operation after ×2 is −2.
• Step 3: Apply: 28 − 2 = 26.

Answer: 26.

Pattern 4: Series of Differences (Second-Level Pattern)

Worked Example: 2, 3, 6, 11, 18, ___

• Step 1: Find the first-level differences: 3 − 2 = 1, 6 − 3 = 3, 11 − 6 = 5, 18 − 11 = 7.
• Step 2: The differences themselves form a pattern: 1, 3, 5, 7 — increasing by 2 each time (the odd numbers). The next difference is 9.
• Step 3: Apply: 18 + 9 = 27.

Answer: 27.

Letter Series: Skip Pattern

Worked Example: A, C, E, G, ___

• Step 1: Convert to positions: A=1, C=3, E=5, G=7.
• Step 2: The positions increase by +2 each time (skipping one letter).
• Step 3: Apply: 7 + 2 = 9, and position 9 is I.

Answer: I.

Letter Series: Reverse Pattern with Increasing Gap

Worked Example: Z, X, U, Q, ___

• Step 1: Convert to positions: Z=26, X=24, U=21, Q=17.
• Step 2: Find the differences (moving backward through the alphabet): 26 − 24 = 2, 24 − 21 = 3, 21 − 17 = 4. The gap increases by 1 each time, and the series moves backward.
• Step 3: The next gap is 5: 17 − 5 = 12, and position 12 is L.

Answer: L.

Common Pitfalls

• Stopping at the first pattern that seems to fit two terms — always confirm it holds for every consecutive pair before committing to an answer.
• Miscounting alphabet positions, especially around the middle of the alphabet (M=13, N=14) — a single miscount throws off the entire answer.
• Forgetting that a series can move backward through the alphabet (as in the Z, X, U, Q example) rather than always increasing.
• Assuming every irregular-looking series must be an alternating pattern — check second-level differences first, since they are common on the CSE-PPT as well.

Exam Strategy

Always test your rule against every pair of consecutive terms, not just the first pair — a rule that fits only the first two terms may be a coincidence. For letter series, writing out the alphabet with numbers 1–26 above each letter on your scratch paper before you start eliminates careless position errors, which are the most common mistake on this question type.