Number Series Reasoning for CLAT | Number & Letter Series

📑 On this page

⚡ The 20-second answer

A series question hides one rule behind a row of terms and asks for the missing one. Climb a fixed ladder: differences, then ratios, then number families (squares, primes, n(n+1)), then split a zig-zag into two chains. Letters are numbers in disguise. The trap: a rule that fits three terms but not all of them.

🎬 The 30-second story

The last padlock at the treasure hunt

“Final lock! The card says 1, 2, 4, __. One number opens it.”

🗝️

Meher

Meher's team reaches the last chest at the college fest.

“Doubling. 8. Done.”

😎

Aarav

Aarav spins the dial. Nothing.

“+1, then +2. Next could be +3. That's 7. Two rules fit three numbers.”

🖊️

Zoya

Zoya writes the gaps under the terms.

“The back of the card says '…, 11, 16'. Gaps +1, +2, +3, +4, +5!”

🔓

Meher

7 opens it. With 8, the gaps would go 1, 2, 4, 3, 5.

Tara's verdict: A rule is proven only when it fits every printed term. Three terms fit many rules; the extra terms decide. Write the difference row first: it settles most series in one line.

How does CLAT word series questions?

Series filled about ten questions across the 2018 and 2019 papers. The stems are short, and each points at a different rung of the ladder below.

Real stem (paper)	Rule inside	Rung that cracks it
Find the missing group: X7D, V11G, T13J, __, P19P (2018 Q91)	Three slots: −2 letters, primes, +3 letters	Slot by slot
Find the missing number: 9, 3, __, 1/3, 1/9 (2018 Q92)	÷ 3 each time	Ratios
Find the next group: CFI, DHL, ILO, LPT, __ (2018 Q94)	Gaps of +3 and +4 inside groups	Letter positions
7, 10, 8, 11, 9, 12, … what comes next? (2018 Q114)	+3, −2 alternating	Split into two chains
Q4RT, __, QRT6, QR7T, Q8RT (2019 Q3)	The number climbs 4 to 8 and walks through the letters	Track the moving part
53, 50, 45, 38, 29, __ (2019 Q12)	Gaps −3, −5, −7, −9	First differences
257, 291, __, 365, 405 (2019 Q4)	Gaps rise by 2	Second differences

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What is the four-check ladder for any series?

Series are built from a small kit of rules, so test them in a fixed order, cheapest first. The order matters: most questions fall at the first rung, and the ones that don't tell you which rung to try next. Here is 2019 Q13 (20, 30, 42, 56, 72, __) on the first rung.

🔢 Series breakdown

The difference row in action (2019 Q13)

2030425672?

1st differences

+10+12+14+16?

2nd differences

+2+2+2?

Rule: Gaps +10, +12, +14, +16 rise by 2, so the next gap is +18: 72 + 18 = 90. The family view agrees: 4×5, 5×6 … 9×10.

1
Differences
Write the gaps between neighbours. Steady? Done. Not steady? Write the gaps of the gaps.
2
Ratios
If terms grow or shrink fast (the last is five or more times the first), divide neighbours: ×2, ÷3, or ×n + k.
3
Families
Look for squares, cubes, primes, n(n+1), or one of these ±1.
4
Split
If the row zig-zags or the gaps are nonsense, read odd and even positions as two separate series.
5
Verify
Test the rule on every printed term, then fill the blank. Letters? Convert to positions before rung one.

💡 The forty-second rule

If no rung has worked after about forty seconds, mark the question and move on. Try the options as a last resort: put each one in the blank and see which gives a clean difference row.

Which number series patterns does CLAT use?

Differences, and differences of differences

🔢 Series breakdown

Second differences: the gaps grow by a constant

47132234?

1st differences

+3+6+9+12?

2nd differences

+3+3+3?

Rule: Gaps +3, +6, +9, +12 grow by 3, so the next gap is +15: 49.

Ratios and mixed operations

Series	Rule	Next
2, 4, 12, 48, 240	×2, ×3, ×4, ×5	×6 = 1,440
3, 7, 15, 31, 63	×2 + 1	127
9, 3, 1, 1/3, 1/9	÷ 3	1/27
2, 3, 8, 27, 112	×1 + 1, ×2 + 2, ×3 + 3…	×5 + 5 = 565

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⚠️ When the answer key slips: 2018 Q92

In 9, 3, __, 1/3, 1/9 every term is a third of the one before, so the blank is 1, printed as option 4 (D). The official key lists '1', which reads as option A (2). The key copied the value, not the option number. A rule you verified on every term beats a misprint.

Number families

🧩 At a glance

Families to recognise on sight

🟦Squares

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

🧊Cubes

1, 8, 27, 64, 125, 216

🔑Primes

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

🤝n(n + 1)

2, 6, 12, 20, 30, 42, 56: gaps are even numbers

±Squares ± 1

0, 3, 8, 15, 24 and 2, 5, 10, 17, 26

🐚Fibonacci

1, 1, 2, 3, 5, 8, 13: each term is the sum of the two before

Two series woven together

🔢 Series breakdown

A zig-zag is two chains

520717914?

1st differences

+15-13+10-8+5?

Rule: The gaps (+15, −13, +10…) are nonsense, so split. Odd places: 5, 7, 9 (+2). Even places: 20, 17, 14 (−3). The blank is the 7th term, so it belongs to the odd chain: 11.

How do letter and alphanumeric series work?

A letter series is a number series written in letters. Convert each letter to its position, solve the numbers, convert back. Use EJOTY (5, 10, 15, 20, 25) to convert in your head, and if a position passes 26, subtract 26: 29 is C.

🔢 Series breakdown

B, E, I, N, __ as numbers

25914?

1st differences

+3+4+5?

Rule: Gaps +3, +4, +5, so +6: 14 + 6 = 20 = T.

Groups like X7D or CFI need one more idea: each slot is its own series. Read the first letters down the row, then the middle parts, then the last letters.

Slot	Terms	Rule	Next
1st letter	A, D, G	+3	J
Number	2, 4, 8	×2	16
Last letter	C, F, I	+3	L
Group	A2C, D4F, G8I		J16L

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Can you solve series questions step by step?

✍️ Worked example Warm-up ⏱ 25 sec

The growing gap

Find the next term: 6, 11, 21, 36, 56, __

1
Differences: +5, +10, +15, +20.
2
Gaps grow by 5, so the next gap is +25.
3
Verify: the rule fits all five terms. 56 + 25 = 81.

Answer: 81

⚡ The exam-hall shortcut

The gaps are the 5-times table. Spot a times table in the gaps and you are done.

✍️ Worked example CLAT level ⏱ 45 sec

Multiply, then add

Find the next term: 2, 3, 8, 27, 112, __

1
Differences: 1, 5, 19, 85. No pattern.
2
Ratios: 112 is 56 times the first term, so the terms multiply. Try ×n + n: 2×1 + 1 = 3, 3×2 + 2 = 8, 8×3 + 3 = 27, 27×4 + 4 = 112.
3
Verify and continue: 112×5 + 5 = 565.

Answer: 565

⚡ The exam-hall shortcut

Each term is roughly the previous one × its position. When the growth explodes, look for ×n.

✍️ Worked example CLAT level ⏱ 30 sec

The term that doesn't belong

Which term is wrong? 3, 9, 27, 81, 242, 729

1
Ratios: 9 ÷ 3 = 3, 27 ÷ 9 = 3, 81 ÷ 27 = 3. The rule is ×3.
2
81 × 3 = 243, not 242. And 243 × 3 = 729, which confirms the rule.
3
Verify: only one term breaks it.

Answer: 242 (it should be 243)

⚡ The exam-hall shortcut

Build the rule from the majority of terms, then hunt the misfit. Never build it from the odd term.

✍️ Worked example Tricky ⏱ 60 sec

Kabir's loyalty stamps

Kabir's café runs a 'stamp storm' for students. In week 1 it hands out 3 bonus stamps, and the totals for the next weeks are 5, 9, 17 and 33. Kabir says the pattern will continue until the reward pool, set at 500 stamps a week, is crossed, and then the scheme stops. In which week will the weekly stamps first cross 500?

1
Differences: 2, 4, 8, 16: they double, so the series grows like powers of 2.
2
Rule: each term = previous × 2 − 1 (3×2 − 1 = 5, 5×2 − 1 = 9).
3
Continue: week 6 = 65, week 7 = 129, week 8 = 257, week 9 = 513.
4
Verify: week 8 (257) is under 500, week 9 (513) is over.

Answer: Week 9 (513 stamps)

⚡ The exam-hall shortcut

Each term is 2ⁿ + 1: week 9 is 512 + 1 = 513.

How did CLAT ask series questions?

Four real questions, one per rung. The 2018 options 1–4 are shown as A–D.

📝 Asked in CLAT 2018 · Q91 Alphanumeric groups

Find the missing group in the sequence: X7D, V11G, T13J, _____, P19P

AQ15M

BR17M

CQ17L

DR15M

Reveal answer + reasoning

Answer: B

Slot by slot. First letters X(24), V(22), T(20), __, P(16): −2 each, so R(18). Numbers 7, 11, 13, __, 19: consecutive primes, so 17. Last letters D(4), G(7), J(10), __, P(16): +3 each, so M(13). R17M, answer B.

Why the others fail

A — Q breaks the −2 letter chain, and 15 is not prime.
C — Q and L each break their chain; only 17 is right.
D — Right letters, but 15 is not prime. The number slot jumps 13 → 17.

📝 Asked in CLAT 2018 · Q94 Letter groups

Find the next group of alphabets: CFI, DHL, ILO, LPT, ________?

AORU

BRUW

COQT

DOSV

Reveal answer + reasoning

Answer: A

Inside each group the gaps are +3 (CFI), +4 (DHL), +3 (ILO), +4 (LPT), so the next is +3. And each group starts with the last letter of the group two places back: ILO starts with CFI's I, LPT with DHL's L, so the next starts with ILO's O. O + 3 = R, R + 3 = U: ORU, answer A.

🔬 Option autopsy

2018 Q94: tap each option

Next group after CFI, DHL, ILO, LPT?

A ORU Tag it

✅ Correct

Starts with O, gaps +3, +3.

B RUW Tag it

❓ Not supported by the text

Starts with R and has gaps +3, +2. Neither part has a rule behind it.

C OQT Tag it

🌗 Half right

Right first letter, wrong gaps (+2, +3).

D OSV Tag it

🌗 Half right

Right first letter, but gaps +4, +3. The +4 turn was LPT's.

✅ Correct❓ Not supported by the text🌗 Half right

Guess the trap behind each option, then tap to check. Wrong options fail in a handful of predictable ways.

📝 Asked in CLAT 2018 · Q114 Alternating series

Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?

B10

C12

D13

Reveal answer + reasoning

Answer: B

The row zig-zags, so split. Odd places: 7, 8, 9. Even places: 10, 11, 12. The next term is the 7th, an odd place, so it continues 7, 8, 9 → 10. The gaps agree: +3, −2 repeating, and 12 − 2 = 10. Answer B.

Why the others fail

A — Restarts the series. Nothing says it loops.
C — Repeats the last term.
D — Continues the even chain (10, 11, 12, 13), but the 7th term belongs to the odd chain.

📝 Asked in CLAT 2019 · Q4 Second differences

Fill in the blank: 257, 291, ________, 365, 405

A313

B322

C327

D343

Reveal answer + reasoning

Answer: C

Our solution (CLAT 2019 has no official key). The known gaps are 291 − 257 = 34 and 405 − 365 = 40. Two missing gaps sit between, and 34, 36, 38, 40 rises evenly: 291 + 36 = 327, and 327 + 38 = 365 checks out. Answer C.

Why the others fail

A — Gaps 34, 22, 52, 40: no pattern.
B — Gaps 34, 31, 43, 40: no pattern.
D — Gaps 34, 52, 22, 40: no pattern.

🔢 Series breakdown

2019 Q4 with the blank filled

257291327365405

1st differences

+34+36+38+40

2nd differences

+2+2+2

Rule: Only 327 makes the gaps rise evenly: +34, +36, +38, +40.

💥 Myth vs fact

Myth vs fact: series

🙅 Myth

If a rule fits three terms, it's the rule.

Tap to bust it →

✅ Fact

1, 2, 4 fits doubling and +1, +2, +3. Test every printed term.

🙅 Myth

Every series is about differences.

Tap to bust it →

✅ Fact

Differences settle about half. Ratios, families and woven chains cover the rest, so climb in order.

🙅 Myth

The answer key is always right.

Tap to bust it →

✅ Fact

2018 Q92's key prints option A for an answer whose value is 1, which is option D.

🙅 Myth

Letter series need a different method.

Tap to bust it →

✅ Fact

Convert letters to positions and it is a number series.

Can you crack these five series?

🎯 Quick quiz

Series quiz

0 / 5

Q1. Find the next term: 3, 8, 15, 24, 35, __

Q2. Find the next letter: D, G, K, P, __

Meher logs how many questions she attempts in her daily sectional mock. Her coaching app hides some days, but shows Day 1: 12, Day 2: 15, Day 3: 21, Day 4: 30 and Day 5: 42. Her mentor says her improvement follows a fixed pattern, and that if she keeps it up she will reach the full sectional target by the end of the week. Meher wants to know what Day 6 should look like.

Q3. If the pattern holds, how many questions will she attempt on Day 6?

Kabir tracks cold-coffee sales at his café across one week. Monday 40, Tuesday 25, Wednesday 44, Thursday 22, Friday 48, Saturday 19. His manager notices that weekday college crowds and evening office crowds alternate, so the numbers form two separate patterns running side by side. Kabir wants to stock the right amount of milk for Sunday, the seventh day in the row.

Q4. If both patterns continue, how many cold coffees will he sell on Sunday?

Q5. Which term is wrong? 2, 6, 12, 20, 30, 41, 56

🎯 Series in a nutshell

Climb the ladder: differences → ratios → families → split.
Second differences catch gaps that grow steadily.
Fast growth means multiplication: try ×n or ×n + k.
A zig-zag is two chains; the blank's position says which chain to extend.
Letters are positions: EJOTY, and subtract 26 past Z.
A rule counts only if it fits every printed term.

📎 Cheat sheet

'Find the missing / next term', gentle growth → differences → first gaps, then gaps of gaps
Terms grow or shrink five times or more → ratios → ×2, ÷3, ×n + k
Row goes up and down → woven series → split odd and even places
Terms sit near 4, 9, 25, 64… → families → n², n³, n² ± 1, n(n + 1), primes
Letters → positions → EJOTY anchors; past 26, subtract 26
Groups like X7D → slots → each slot is its own series
'Which term is wrong?' → majority rule → build the rule from the other terms, find the misfit

Frequently asked questions

How do you solve number series questions quickly?

Test rules in a fixed order. Write the differences first, and if they are not steady write the second differences. If the terms grow fast, divide neighbours. Then look for squares, cubes, primes or n(n + 1). If the row zig-zags, split it into two series. Most questions fall at the first step.

How do I solve letter series in reasoning?

Turn each letter into its position in the alphabet, A = 1 to Z = 26, and solve the numbers as an ordinary series. Then turn the answer back into a letter. EJOTY (5, 10, 15, 20, 25) makes the conversion quick, and if a position passes 26, subtract 26.

What if the differences make no sense?

Nonsense differences usually mean one of two things. If the terms grow quickly, the rule is multiplication, so try ratios. If the terms go up and down, two series are woven together: read the odd places and the even places separately, and extend the chain that the blank belongs to.

Does CLAT still ask number and letter series?

Series were a regular part of the 2018 and 2019 papers. Since 2020, Logical Reasoning has been passage-based, but CLAT 2025 brought a seating set back, so short analytical questions can return. One series question is quick marks for anyone with a method.

Was the CLAT 2018 Q92 answer key wrong?

Yes, it was a slip. The series 9, 3, __, 1/3, 1/9 divides by 3 each time, so the blank is 1, which was option 4. The key lists 1 as the option number, which points to option A (2). The rule-verified answer is 1, option D.