Missing Number Series Tricks for Bank Exams
To solve a missing number series quickly, look at how fast the numbers grow: slow growth means addition or subtraction (check differences), fast growth means multiplication (check ratios), and growth near squares or cubes means n² or n³ patterns. Then test the rule on every term before choosing the answer.
🔥 Key Exam Takeaway (4-step method): (1) Check the growth speed. (2) Write the differences; if they are not constant, take differences again or compare them with squares, cubes, primes or powers of 2. (3) If numbers roughly double or triple, test ×n ± k patterns. (4) If terms jump up and down, split into two alternate series. Always confirm the rule on all given terms.
Number series gives about 5 questions in IBPS and SBI Clerk and PO prelims (missing-number or wrong-number type). The series below are checked in Python term by term.
Types of Number Series Asked in Bank Exams
| # | Pattern type | Clue | Example | Next term |
|---|---|---|---|---|
| 1 | Constant or growing difference | Slow, steady growth | 5, 9, 17, 29, 45, ? | 65 |
| 2 | Difference = powers of 2 | Differences 2, 4, 8, 16 | 7, 9, 13, 21, 37, ? | 69 |
| 3 | Difference = squares | Differences 1, 4, 9, 16 | 11, 12, 16, 25, 41, ? | 66 |
| 4 | Difference = primes | Differences 3, 5, 7, 11, 13 | 2, 5, 10, 17, 28, ? | 41 |
| 5 | Squares / cubes ± k | Terms near 4, 9, 16 or 8, 27, 64 | 3, 8, 15, 24, 35, ? | 48 |
| 6 | Constant multiply ± k | Each term about double or triple | 5, 11, 23, 47, 95, ? | 191 |
| 7 | Multiply by 1, 2, 3 … + k | Growth speeds up sharply | 2, 3, 8, 27, 112, ? | 565 |
| 8 | Multiply by 1.5, 2, 2.5 … | Ratios rise by 0.5 | 4, 6, 12, 30, 90, ? | 315 |
| 9 | Division pattern | Terms fall sharply | 240, 120, 40, 10, 2, ? | 1/3 |
| 10 | Alternate (two series) | Up-down movement | 10, 5, 20, 10, 40, 20, ? | 80 |
How to Find the Pattern in Number Series (Step-by-Step Trick)
Step 1: Judge the Growth Speed
- Last term less than about 3 times the first in a 6-term series → think differences.
- Last term 10 to 100 times the first → think multiplication.
- Terms close to perfect squares or cubes → think n² ± k or n³ ± k.
Step 2: Write First Differences, Then Second Differences
For 5, 9, 17, 29, 45: first differences 4, 8, 12, 16 → these increase by 4 → next difference 20 → 65.
Step 3: Test Ratios for Fast Series
For 4, 6, 12, 30, 90: ratios 1.5, 2, 2.5, 3 → next ratio 3.5 → 90 × 3.5 = 315.
Step 4: Split Jumping Series
For 10, 5, 20, 10, 40, 20, ?: odd positions 10, 20, 40 (× 2); even positions 5, 10, 20 (× 2) → next odd term 80.
Number Series Formulas and Patterns to Memorise
| Know these | Values |
|---|---|
| Squares 1 to 20 | 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400 |
| Cubes 1 to 12 | 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728 |
| Primes up to 50 | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 |
| Powers of 2 | 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 |
| n³ + n² | 2, 12, 36, 80, 150, 252 |
| n² − 1 | 0, 3, 8, 15, 24, 35, 48 |
Missing Number Series Questions for Bank Exams with Solutions
Q1. 3, 8, 15, 24, 35, ? Solution: n² − 1 for n = 2 to 6: 4 − 1, 9 − 1, 16 − 1, 25 − 1, 36 − 1. Next: 49 − 1 = 48.
Q2. 5, 11, 23, 47, 95, ? Solution: × 2 + 1 each time. 95 × 2 + 1 = 191.
Q3. 2, 3, 8, 27, 112, ? Solution: × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4 → 112 × 5 + 5 = 565.
Q4. 4, 6, 12, 30, 90, ? Solution: × 1.5, × 2, × 2.5, × 3 → × 3.5: 90 × 3.5 = 315.
Q5. 7, 9, 13, 21, 37, ? Solution: differences 2, 4, 8, 16 → 32. 37 + 32 = 69.
Q6. 120, 99, 80, 63, 48, ? Solution: 11² − 1, 10² − 1, 9² − 1, 8² − 1, 7² − 1 → 6² − 1 = 35.
Q7. 1, 9, 25, 49, 81, ? Solution: squares of odd numbers 1, 3, 5, 7, 9 → 11² = 121.
Q8. 2, 12, 36, 80, 150, ? Solution: n³ + n²: 1 + 1, 8 + 4, 27 + 9, 64 + 16, 125 + 25 → 216 + 36 = 252.
Q9. 6, 7, 16, 51, 208, ? Solution: × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4 → 208 × 5 + 5 = 1045.
Q10. 5, 9, 17, 29, 45, ? Solution: differences 4, 8, 12, 16 → 20. 45 + 20 = 65.
Q11. 2, 5, 10, 17, 28, ? Solution: differences 3, 5, 7, 11 are consecutive primes → next 13. 28 + 13 = 41.
Q12. 8, 12, ?, 60, 180 (missing term in the middle) Solution: × 1.5, × 2, × 2.5, × 3. 12 × 2 = 24 (check: 24 × 2.5 = 60, 60 × 3 = 180 ✔).
Q13. 7, 26, 63, 124, ? Solution: n³ − 1 for n = 2 to 5 → 6³ − 1 = 215.
Q14. 3, 8, 23, 68, 203, ? Solution: × 3 − 1 each time → 203 × 3 − 1 = 608.
Q15. 11, 12, 16, 25, 41, ? Solution: differences 1, 4, 9, 16 (squares) → 25. 41 + 25 = 66.
Mixed-Pattern Number Series (SBI and IBPS PO Level)
PO-level papers combine two operations. These six are typical:
Q16. 12, 13, 28, 87, 352, ? Solution: × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4 → 352 × 5 + 5 = 1765.
Q17. 3, 10, 29, 66, 127, ? Solution: n³ + 2 for n = 1 to 5 → 6³ + 2 = 218.
Q18. 1, 3, 9, 31, 129, ? Solution: × 1 + 2, × 2 + 3, × 3 + 4, × 4 + 5 → 129 × 5 + 6 = 651.
Q19. 200, 196, 180, 144, 80, ? Solution: subtract squares of even numbers: − 2², − 4², − 6², − 8² → − 10² = − 100. 80 − 100 = −20.
Q20. 15, 16, 34, 105, 424, ? Solution: × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4 → 424 × 5 + 5 = 2125.
Q21. 4, 5, 13, 40, 104, ? Solution: differences 1, 8, 27, 64 (cubes) → next 125. 104 + 125 = 229.
Number Series Strategy for SBI Clerk and IBPS Clerk 2026
- Read all five series first and solve the ones whose pattern you see at a glance. Usually two or three are direct.
- Use the last two terms to guess the operation. If the last term is about 5 times the previous one, test × 5 ± k.
- Work backwards for middle-missing series: the terms after the gap confirm the rule.
- Keep a 40-second limit per series in prelims. A skipped series costs nothing; a 3-minute struggle costs two other questions.
- Practise 10 series a day for two weeks; the same 10 pattern families repeat across papers.
Wrong Number Series Tricks (Related Question Type)
In wrong-number series, one term breaks the rule. Find the rule from the majority of terms, then check each term.
Example: 5, 11, 23, 46, 95, 191 → the rule × 2 + 1 fits 5 → 11 → 23, but 23 × 2 + 1 = 47, not 46. The wrong term is 46. (95 × 2 + 1 = 191 confirms the rule.)
Example: 2, 5, 10, 17, 26, 41 → differences 3, 5, 7, 9, 15. With primes the differences should be 3, 5, 7, 11, 13, giving 2, 5, 10, 17, 28, 41. The wrong term is 26 (should be 28).
Number Series Quick Revision Table
| What you see | First thing to test |
|---|---|
| Small, steady increases | First and second differences |
| Differences 2, 4, 8, 16 | Powers of 2 |
| Differences 1, 4, 9, 16 or 1, 8, 27, 64 | Squares or cubes as differences |
| Differences 2, 3, 5, 7, 11 | Consecutive primes |
| Terms near 4, 9, 16, 25 or 8, 27, 64 | n² ± k or n³ ± k |
| Each term about double / triple | × 2 ± k or × 3 ± k |
| Growth that keeps speeding up | × 1, × 2, × 3 … with + k |
| Ratios 1.5, 2, 2.5 | Multipliers rising by 0.5 |
| Terms falling sharply | ÷ 2, ÷ 3, ÷ 4 … |
| Up-down zig-zag | Two alternate series |
Common Mistakes in Missing Number Series
| Mistake | Fix |
|---|---|
| Choosing the first rule that fits two terms | Confirm the rule on every given term |
| Missing alternate series | If the series zig-zags, split odd and even positions |
| Ignoring decimal multipliers (× 1.5, × 2.5) | Divide consecutive terms when growth is irregular but fast |
| Not checking second differences | If first differences are uneven, find their differences |
| Wasting time on one hard series | Skip after 40 seconds and return at the end |
Number Series Practice Questions (with Answers)
- 4, 10, 22, 46, 94, ? → 190 (× 2 + 2)
- 3, 4, 8, 17, 33, ? → 58 (differences 1, 4, 9, 16, 25)
- 1000, 500, 250, 125, 62.5, ? → 31.25 (÷ 2)
- 2, 5, 12, 27, 58, ? → 121 (× 2 + 1, × 2 + 2, × 2 + 3, × 2 + 4, × 2 + 5)
- 17, 16, 8, −19, ? → −83 (− 1³, − 2³, − 3³, − 4³)
- 9, 28, 65, 126, ? → 217 (n³ + 1 for n = 2 to 6)
- 6, 3, 12, 6, 24, 12, ? → 48 (alternate series × 2)
- 1, 2, 6, 24, 120, ? → 720 (× 2, × 3, × 4, × 5, × 6)
Number Series FAQs
How many number series questions come in SBI Clerk prelims?
Usually about 5 questions, either missing-number or wrong-number type, though the pattern can change by year.
What is the fastest trick for number series?
Judge the growth first. Slow growth: check differences. Fast growth: check ratios (× n ± k). Near squares or cubes: check n² ± k or n³ ± k.
What is the difference between missing and wrong number series?
In a missing number series you find the next or middle term. In a wrong number series all terms are given and you find the one that breaks the rule.
How much time should I spend on one series question?
Aim for 20 to 30 seconds. If no pattern appears in about 40 seconds, move on and come back later.
What should I do if two rules fit the series?
Check which rule also fits the first and last given terms and gives one of the options. Exam setters design one clear rule; if two seem to fit, one usually fails on an early term.
Which number series patterns are most common in IBPS Clerk?
Differences (constant, squares, cubes, primes), × n ± k patterns and n² or n³ ± k patterns appear most often. Alternate series and decimal multipliers are less common but do appear.
Are number series in SSC and bank exams the same?
The patterns are similar, but bank exams use bigger numbers and mixed patterns (× n + n, decimal multipliers), while SSC reasoning often mixes in letters and alphanumeric series.
Related topics: revise wrong number series for bank exams, approximation questions for bank exams and alphanumeric series tricks for bank exams next.
Practice Next
- Number series practice: IBPS PO Number Series Mock Test 01 and IBPS Clerk Number Series Mock Test 02 (missing and wrong number).
- Topic test: SBI PO Mock Test: Quantitative Aptitude Number Series and SSC CGL Number Series Mock Test 01.
- Full section: IBPS PO Quantitative Aptitude Sectional Mock Test 02.
- New topic-wise test: IBPS Clerk Number Series Mock Test 01: Missing and Wrong Number Series (15 Questions).
- New SSC topic test: SSC CHSL Number and Alphabet Series Mock Test 01: Missing Number and Letter Series (15 Questions).
- Timed practice: SBI PO Quant Mini Quiz 01 and IBPS PO Quant Mini Quiz 01.
- Related notes: Simplification Tricks for Bank Exams, Quadratic Equation Tricks for Bank Exams and Unit Digit Tricks for SSC CGL.
- Open recruitment: SBI Clerk Recruitment 2026.
- Browse all study notes.