लुप्त पद

हिंदी में पढ़ें

Missing Term (लुप्त पद)

Chapter Outline & Learning Goals

By the end of this chapter you will be able to:

1. Find the missing term in number series built on differences, ratios, powers and mixed operations.
2. Crack letter and alphanumeric series by turning letters into numbers.
3. Solve missing-number figures and 3×3 grids where each row or column hides one rule.
4. Spot the "wrong term" in a series that looks correct at first glance.
5. Use a fixed checking order so you never stare at a question without a plan.

1. The Hook: The Detective's Last Clue

Imagine a detective's notebook: 2, 6, 12, 20, 30, ___. Every number is a footprint, and one footprint is missing. The criminal (the rule) has walked the same way every time — you only have to notice the stride.

That is all a missing-term question is: a pattern with one hole. The examiner hides the rule, and you have about 40 seconds to find it. The good news? At Graduation level the rules come from a small family — once you know the family, you recognise every member.

2. "I Can't See the Pattern!" — The Common Struggle

Most students lose marks here for three reasons:

• They guess the rule from two terms and stop checking.
• They jump to complicated ideas (cubes, primes) before trying the simple ones (differences).
• They miscount letter positions (A = 1, not 0).

If you have felt stuck, it is not a talent problem — it is an order problem. This chapter gives you an order.

🧠 Active Recall: Without looking up, name the three reasons students get stuck. Which one have you done before?

3. Chunk 1 — Number Series: The Five Families

(a) Difference series

Write the differences between neighbours.

• 3, 7, 13, 21, 31, ? → differences 4, 6, 8, 10 → next difference 12 → 43.
• If the first differences are not regular, take second differences: 2, 5, 11, 20, 32, ? → 3, 6, 9, 12 → next 15 → 47.

(b) Ratio (multiplication) series

Divide each term by the previous one.

• 5, 15, 45, 135, ? → ×3 → 405.
• Changing ratio: 2, 2, 4, 12, 48, ? → ×1, ×2, ×3, ×4 → ×5 → 240.

(c) Powers: squares and cubes

• 4, 9, 25, 49, 121, ? → squares of primes 2, 3, 5, 7, 11 → 13² = 169.
• 0, 7, 26, 63, 124, ? → n³ − 1 → 6³ − 1 = 215.

(d) Mixed operations

The terms grow too fast for differences but the ratio is not fixed: try "× something, ± something".

• 3, 7, 15, 31, 63, ? → ×2 + 1 → 127.
• 2, 5, 14, 41, 122, ? → ×3 − 1 → 365.

(e) Two series in one (alternate terms)

Odd positions follow one rule, even positions another.

• 2, 10, 4, 20, 8, 40, ? → odd places 2, 4, 8 (×2) → 16.

🧠 Active Recall: For 6, 11, 21, 41, 81, ? — which family is it? (Answer: ×2 − 1 → 161.)

4. Chunk 2 — Letter Series: Change Letters into Numbers

Always convert with A = 1 … Z = 26. Remember the anchors with the mnemonic "EJOTY": E = 5, J = 10, O = 15, T = 20, Y = 25.

• B, E, I, N, ? → 2, 5, 9, 14 → differences 3, 4, 5 → next 6 → 20 = T.
• Z, X, U, Q, ? → 26, 24, 21, 17 → −2, −3, −4 → −5 → 12 = L.
• Letter groups: AZ, BY, CX, ? → first letter moves forward, second backward (opposite pairs add to 27) → DW.

Wrap-around: after Z comes A again (26 + 1 → 1).

5. Chunk 3 — Alphanumeric Series

Treat each part as its own series.

• A1, C3, E5, G7, ? → letters skip one (A, C, E, G, I), numbers are odd → I9.
• 3C, 5E, 8H, 12L, ? → numbers grow by +2, +3, +4, so next +5 = 17; each letter is the letter at that number's position (3 = C, 5 = E, 8 = H, 12 = L) → 17Q.

🧠 Active Recall: What is the position of R? (Hint: T = 20, so R = 18.)

6. Chunk 4 — Missing Numbers in Figures and Grids

In a 3×3 grid, test rows first, then columns:

Row rule: first × second = third → 7 × 8 = 56.

Common grid rules: sum of a row is constant; third = (first + second) × k; middle = average of the other two; squares of the first two add up to the third.

In circle or triangle figures, the centre number is usually made from the outer numbers (sum, product, or difference). Check every figure — the rule must fit all of them, not just one.

7. Chunk 5 — The Wrong Term

"Find the term that does not fit": 3, 5, 9, 17, 31, 65.
Rule ×2 − 1: 3, 5, 9, 17, 33, 65 → 31 is the wrong term.
Trick: find the rule using the terms that clearly agree, then test each term one by one.

8. The Fixed Checking Order (Mnemonic: "D-R-P-M-A")

1. Differences (first, then second)
2. Ratios
3. Powers (squares, cubes, ± a small number)
4. Mixed (× then ±)
5. Alternate terms (two series)

Spend at most 15 seconds per step. If nothing appears after the fifth step, move on and come back later.

9. Summary Table

📅 Review this chapter after 2 days, then try one practice set without looking at the table.

⚠️ Caution: Examiner's Trap

1. Two rules fit the given terms. 1, 2, 4, ? could be ×2 (→ 8) or +1, +2, +3 (→ 7). Only one of them is in the options — always check the options before you commit.
2. The rule changes in the last step. A series looks like ×2 for three terms and then becomes ×2 + 2. Test the rule on every given term, not only the first three.
3. Off-by-one letters. Counting A = 0 gives an answer exactly one letter away — and that wrong letter is always in the options.