Number and letter series for RRB Group D

Series questions give you a row of numbers or letters built by a rule, and ask for the next term, a missing term or the one term that breaks the rule. They are among the quickest questions in the reasoning section once you have a routine.

Without a routine, a candidate stares at the numbers hoping the pattern will jump out. With one, they run through the same five checks every time, and most series give way within the first two. This guide gives you that routine, the patterns it finds, and a practice set.

The checking order

1. Differences: subtract each term from the next. Are the differences constant, or do they themselves form a pattern (2, 4, 6, 8 or 3, 6, 12, 24)?
2. Multiplication or division: is each term a fixed multiple of the one before?
3. Squares and cubes: are the terms equal to, or close to, 1, 4, 9, 16, 25… or 1, 8, 27, 64, 125…?
4. Mixed rules: × 2 + 1, × 3 − 1, or a multiplier that grows (× 1 + 1, × 2 + 2, × 3 + 3).
5. Two series mixed together: look at the odd places and the even places separately.

The main number patterns

Letter series

Turn every letter into its position (A = 1, B = 2, … Z = 26) and run the same checks. If you go past Z, start again at A (so 27 means A again, 28 means B).

• Learn the anchors E = 5, J = 10, O = 15, T = 20, Y = 25 (EJOTY).
• For backward series, the gaps are negative: Z, W, T is −3 each time.
• In letter–number series such as B2, E5, H8, check the letters and the numbers separately. Often the number is simply the letter's position.
• In letter groups such as AB, EF, IJ, check the first letters of each group as one series.

Our reasoning plan has more on learning letter positions quickly.

Wrong-term questions

Here the series has one term that does not fit. Find the rule from the terms that agree, then check each term in turn. The rule usually shows which term is wrong and what it should have been. When the wrong term is in the middle, the term after it still follows the correct value, which confirms your answer.

Worked examples

Example 1: 3, 7, 15, 31, ?

• Differences are 4, 8, 16, which double. So the next difference is 32, and the answer is 31 + 32 = 63.
• The same series is also "× 2 + 1": 31 × 2 + 1 = 63. Both views agree.

Example 2: 6, 11, 21, 36, 56, ?

• Differences: 5, 10, 15, 20. The next difference is 25.
• 56 + 25 = 81.

Example 3: 1, 2, 6, 21, 88, ?

• The terms grow faster and faster, so try mixed rules. 1 × 1 + 1 = 2, 2 × 2 + 2 = 6, 6 × 3 + 3 = 21, 21 × 4 + 4 = 88.
• Next: 88 × 5 + 5 = 445.

Example 4: 2, 10, 4, 20, 6, 30, ?

• The terms jump up and down, so split them. Odd places: 2, 4, 6. Even places: 10, 20, 30.
• The missing term is the 7th, an odd place, so it continues 2, 4, 6: answer 8.

Example 5: Z, X, U, Q, ?

• Positions: 26, 24, 21, 17. Gaps: −2, −3, −4. The next gap is −5.
• 17 − 5 = 12, which is L.

Example 6 (wrong term): 2, 5, 11, 23, 48, 95

• Rule from the first four terms: × 2 + 1 (2 → 5 → 11 → 23).
• 23 × 2 + 1 = 47, not 48. And 47 × 2 + 1 = 95, which matches the last term.
• The wrong term is 48; it should be 47.

Common mistakes

• Checking the rule on the first two or three terms only. The rule must fit every term.
• Missing an alternating series because the ups and downs looked random.
• Counting letters on your fingers, and slipping by one.
• Forgetting to wrap round after Z in letter series.
• In wrong-term questions, marking the term just after the real mistake. Check each term against the correct value, not against the wrong one before it.

Practice set

1. 4, 8, 16, 32, ?
2. 1, 3, 6, 10, 15, ?
3. 2, 6, 12, 20, 30, ?
4. Z, W, T, Q, ?
5. Find the wrong term: 1, 8, 27, 64, 124
6. B2, E5, H8, ?
7. 5, 9, 17, 33, 65, ?
8. 7, 14, ?, 56, 112

Answers:

1. 64. Each term doubles.
2. 21. Differences 2, 3, 4, 5, so the next difference is 6.
3. 42. Differences 4, 6, 8, 10, then 12. It is also 6 × 7.
4. N. Positions 26, 23, 20, 17, then 14. Each step is −3.
5. 124. The terms are cubes, and 5³ = 125.
6. K11. Letters move +3 (B, E, H, K), and each number is the letter's position.
7. 129. Differences 4, 8, 16, 32 double, so the next is 64. It is also × 2 − 1.
8. 28. Each term doubles: 14 × 2 = 28, and 28 × 2 = 56.

What to do next

• Learn EJOTY and write the positions of all 26 letters from memory once.
• Solve 15 series questions a day for a week, running the five checks in order.
• Keep a list of every new pattern you meet, with one example of each.
• Next, apply the same letter skills to coding–decoding.