Number series for bank exams looks hard only until you know the patterns. Almost every series in IBPS PO, SBI PO, IBPS Clerk and RBI Assistant exams is built from a small set of ideas: differences, multipliers, squares, cubes, alternating logic or sums of earlier terms. This guide explains the 12 number series patterns that are commonly practiced for Prelims and Mains, a fast method to identify the pattern in under 20 seconds, and a practice set with answers. Scroll to the end to download the free practice set PDF.
Table of Contents
How to Identify the Pattern: The 4-Step Method
Run the same checks in the same order every time.
- Look at the growth. Slow growth usually means addition or differences. Fast growth usually means multiplication, squares or cubes.
- Write the differences between consecutive terms. If they are constant, you are done. If they change, check the differences of the differences.
- Write the ratios (divide each term by the previous one). If they are constant or follow a simple order (×2, ×3, ×4), you have the pattern.
- Check nearness to squares and cubes, and check whether odd and even positions behave differently (alternating series).
Quick recognition table
| What you see | Try first |
|---|---|
| Terms rise slowly and differences grow by a fixed amount | Second-order differences |
| Terms double or triple quickly | Multiplier series or ×n + k |
| Terms are close to 25, 36, 49 or 27, 64, 125 | Squares or cubes ± constant |
| Terms go up and down | Alternating or two interleaved series |
| Terms fall quickly | Division series |
| Each term is about the sum of the last two | Fibonacci type |
Revise the squares and cubes table before you start. It makes patterns 8 and 9 almost instant.
12 Number Series Patterns with Solved Examples
Pattern 1: Constant difference series
Each term increases (or decreases) by the same number.
Example: 7, 12, 17, 22, 27, ?
Difference is +5 every time. Next term = 27 + 5 = 32
Pattern 2: Increasing differences (second-order differences)
The differences themselves follow a pattern.
Example: 3, 5, 9, 15, 23, ?
Differences: 2, 4, 6, 8, so the next difference is 10. Next term = 23 + 10 = 33
Pattern 3: Prime-number differences
The differences are consecutive prime numbers.
Example: 5, 8, 13, 20, 31, ?
Differences: 3, 5, 7, 11, so the next difference is 13. Next term = 31 + 13 = 44
Pattern 4: Constant multiplier series
Each term is multiplied by the same number.
Example: 3, 6, 12, 24, 48, ?
Multiplier is ×2. Next term = 48 × 2 = 96
Pattern 5: Increasing multiplier series
The multiplier increases by 1 each step.
Example: 3, 6, 18, 72, 360, ?
Multipliers: ×2, ×3, ×4, ×5, so the next multiplier is ×6. Next term = 360 × 6 = 2160
Pattern 6: Multiply and add (or subtract)
Each term is multiplied by a fixed number and a fixed number is added or subtracted.
Example: 3, 7, 15, 31, 63, ?
Pattern: ×2 + 1. Check: 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31. Next term = 63 × 2 + 1 = 127
Pattern 7: ×n + n (changing multiplier with matching addition)
The multiplier and the number added both increase by 1 each step. This is a favourite in Mains.
Example: 2, 3, 8, 27, 112, ?
Pattern: ×1 + 1, ×2 + 2, ×3 + 3, ×4 + 4. Check: 2 × 1 + 1 = 3, 3 × 2 + 2 = 8, 8 × 3 + 3 = 27, 27 × 4 + 4 = 112. Next term = 112 × 5 + 5 = 565
Pattern 8: Squares ± constant
Each term is a perfect square plus or minus a number.
Example: 10, 17, 26, 37, 50, ?
Pattern: n² + 1 for n = 3, 4, 5, 6, 7 (9 + 1, 16 + 1, 25 + 1, 36 + 1, 49 + 1). Next term = 8² + 1 = 65
Pattern 9: Cubes ± constant
Each term is a perfect cube plus or minus a number.
Example: 9, 28, 65, 126, 217, ?
Pattern: n³ + 1 for n = 2, 3, 4, 5, 6 (8 + 1, 27 + 1, 64 + 1, 125 + 1, 216 + 1). Next term = 7³ + 1 = 344
Pattern 10: Alternating series (two interleaved series)
Odd-position terms follow one rule and even-position terms follow another.
Example: 5, 8, 10, 16, 15, 32, 20, ?
- Odd positions: 5, 10, 15, 20 (add 5)
- Even positions: 8, 16, 32 (multiply by 2)
The missing term is in an even position, so next = 32 × 2 = 64
Pattern 11: Division series
Each term is divided by a decreasing (or increasing) number.
Example: 5760, 960, 192, 48, 16, ?
Divisors: ÷6, ÷5, ÷4, ÷3, so the next divisor is ÷2. Next term = 16 ÷ 2 = 8
Pattern 12: Sum of previous terms (Fibonacci type)
Each term is the sum of the two terms before it.
Example: 3, 4, 7, 11, 18, ?
Check: 3 + 4 = 7, 4 + 7 = 11, 7 + 11 = 18. Next term = 11 + 18 = 29
Bonus pattern (n × (n + 1)): 2, 6, 12, 20, 30, ? is 1×2, 2×3, 3×4, 4×5, 5×6, so the next term is 6 × 7 = 42.
Number Series Tricks to Save Time
- Start with differences, then ratios. These two checks solve most series in under 20 seconds.
- Do not hunt for a complex rule first. The simple rule is usually the right one.
- Test your pattern on every term, not just the first two. A rule that fits only part of the series is wrong.
- Memorize squares up to 30 and cubes up to 15. Pattern 8 and 9 questions become instant. (The speed of solving questions increases, and time is also saved.)
- If you are stuck for more than 40 seconds, skip the question and come back at the end. ( I did not skip the question, and this wasted time that I could have otherwise spent on other questions.)
Common Mistakes in Number Series
- Stopping at the first rule that fits two terms. Always verify the full series.
- Missing alternating patterns. If the series zigzags, split it into odd and even positions.
- Ignoring the +n part in ×n + n series. Both the multiplier and the addition change.
- Calculation slips. Most wrong answers in number series are arithmetic errors, not pattern errors.
Practice Set (30 to 40 seconds each)
Find the missing number.
- 11, 14, 19, 26, 35, ?
- 6, 7, 16, 51, 208, ?
- 2, 10, 50, 250, 1250, ?
- 3, 8, 15, 24, 35, ?
- 7, 14, 12, 24, 22, 44, ?
- 4, 5, 9, 14, 23, 37, ?
- 4320, 720, 144, 36, 12, ?
- 7, 26, 63, 124, 215, ?
Answers and Explanations
- 46. Differences 3, 5, 7, 9, so the next is 11. 35 + 11 = 46. (Pattern 2)
- 1045. ×1 + 1, ×2 + 2, ×3 + 3, ×4 + 4, ×5 + 5. 208 × 5 + 5 = 1045. (Pattern 7)
- 6250. Multiplier ×5. 1250 × 5 = 6250. (Pattern 4)
- 48. n² − 1 for n = 2 to 6, so next is 7² − 1 = 48. (Pattern 8)
- 42. ×2, −2, ×2, −2, ×2, −2. 44 − 2 = 42. (Alternating operations)
- 60. Each term is the sum of the previous two. 23 + 37 = 60. (Pattern 12)
- 6. Divisors ÷6, ÷5, ÷4, ÷3, ÷2. 12 ÷ 2 = 6. (Pattern 11)
- 342. n³ − 1 for n = 2 to 6, so next is 7³ − 1 = 342. (Pattern 9)
Download Number Series Questions PDF
Get the number series practice set PDF with all 12 patterns, solved examples and 8 practice questions, and practice offline with a timer.
👉 [Download Number Series Questions PDF] (join our Telegram community to get the link)
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- Squares and Cubes Chart for Bank Exams (Free PDF)
- Approximation and Simplification Tricks for Bank Exams
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Next post: Missing and Wrong Number Series: Tricks + Practice Set
FAQs on Number Series for Bank Exams
Are number series asked in IBPS PO and SBI PO?
Number series is a regularly practiced topic for bank exams, but the exact pattern changes from year to year. Check the latest exam notification and the previous year’s paper to see how it is being asked now.
How many number series patterns should I learn?
The 12 patterns in this post cover most questions. With regular practice you will also recognize combinations of two patterns.
What is the fastest way to find the pattern?
Check differences first, then ratios, then nearness to squares and cubes, and finally whether odd and even positions behave differently.
How much time should I spend on one number series question?
Aim for 30 to 40 seconds once you are comfortable, and skip the question if you are stuck beyond that.
