Number series for IBPS Clerk

Number series questions come in two forms. In a missing number series you find the next term (or a term in the middle). In a wrong number series one term breaks the pattern and you find it. Both usually appear as a block of questions in the clerk prelims, and each should take 25–40 seconds.

That sounds tight, but clerk-level series are built from a small set of patterns. If you check them in a fixed order, most series give themselves up within three or four quick calculations. The ones that do not are the ones to skip.

The first look: how fast do the terms grow?

Before any calculation, look at the size of the numbers.

• Slow growth (7, 10, 16, 25, 37) points to addition or subtraction. Check differences.
• Fast growth (5, 9, 17, 33, 65 or 2, 6, 24, 120) points to multiplication. Check ratios.
• Up and down (2, 10, 4, 20, 8) points to two series interleaved. Check alternate terms.
• Very fast growth (5, 6, 14, 45, 184) points to multiplication plus addition, often with a rising multiplier.

This first look takes two seconds and saves you trying the wrong family of rules.

A checking routine

1. First differences. Subtract each term from the next. Constant? Rising by a fixed step? Squares, cubes, primes?
2. Second differences. If the first differences are not obvious, take their differences. A constant or simple second difference means the series is built on a steadily changing step.
3. Ratios. Is each term roughly 2×, 3×, … the last? Then test "× n + k" or "× n − k".
4. Rising multipliers. × 1, × 2, × 3 … or × 0.5, × 1.5, × 2.5 …, sometimes with an added number.
5. Squares and cubes. Are the terms themselves squares or cubes, or one more or less than them?
6. Alternate terms. Do odd and even positions form two separate series?

Why the order works: differences and ratios cover most clerk series, so you check them first. The rarer patterns come later, so you do not waste time on them when a simple rule fits.

Standard sequences to know on sight

If a list of differences matches one of these rows, you have found the pattern.

Worked examples

Example 1 (differences). 7, 10, 16, 25, 37, ?

1. Differences: 3, 6, 9, 12. They rise by 3.
2. Next difference: 15.
3. Answer: 37 + 15 = 52.

Example 2 (second differences). 4, 6, 11, 21, 38, ?

1. First differences: 2, 5, 10, 17. Not constant, not doubling.
2. Second differences: 3, 5, 7. Odd numbers, so the next is 9, and the next first difference is 17 + 9 = 26.
3. Answer: 38 + 26 = 64.
4. Check with the table: 2, 5, 10, 17, 26 is n² + 1. Two routes, same answer.

Example 3 (× n + n). 5, 6, 14, 45, 184, ?

1. Growth is very fast, so test multiplication with addition.
2. 5 × 1 + 1 = 6; 6 × 2 + 2 = 14; 14 × 3 + 3 = 45; 45 × 4 + 4 = 184.
3. Answer: 184 × 5 + 5 = 925.

Example 4 (decimal multipliers). 64, 32, 48, 120, 420, ?

1. The series falls and then rises fast, so check ratios: 32 ÷ 64 = 0.5; 48 ÷ 32 = 1.5; 120 ÷ 48 = 2.5; 420 ÷ 120 = 3.5.
2. Multipliers rise by 1 each time. Next is × 4.5.
3. Answer: 420 × 4.5 = 1,890.

Example 5 (prime differences). 10, 12, 15, 20, 27, 38, ?

1. Differences: 2, 3, 5, 7, 11. These are consecutive primes.
2. Next prime: 13.
3. Answer: 38 + 13 = 51.

Example 6 (alternate terms). 2, 10, 4, 20, 8, 40, ?

1. Odd positions: 2, 4, 8, doubling. Even positions: 10, 20, 40, doubling.
2. The seventh term is in an odd position, so it continues 2, 4, 8.
3. Answer: 16.

Example 7 (wrong term). 4, 9, 19, 39, 78, 159

1. The terms roughly double. Test × 2 + 1: 4 → 9 → 19 → 39 → 79.
2. The series shows 78 where the rule gives 79.
3. Check the rule on the last term too: 79 × 2 + 1 = 159. It fits.
4. The wrong term is 78.

Wrong-term questions: a method

• Find the rule using the terms that agree. With six terms, four or five will fit one rule.
• The wrong term is usually close to the correct value, off by 1, 2 or a small amount. That makes it easy to miss if you check only roughly.
• Always check the terms after the suspect. If the rule works from the correct value onward, you have the right answer. If you "correct" a term and the next one then fails, your rule is wrong.
• Watch the first and last terms. Candidates often check the middle carefully and forget the ends.

When to skip

If two passes through the routine (about 30 seconds) have not found the pattern, mark it and move on. A series block usually has a mix of easy and hard series. Taking all the easy ones and skipping one hard one is better than getting stuck on the hard one and rushing the rest.

Practice

Set a 4-minute timer.

1. 11, 13, 17, 23, 31, ?
2. 6, 11, 21, 41, 81, ?
3. 1, 2, 6, 24, 120, ?
4. 150, 146, 137, 121, 96, ?
5. Find the wrong term: 3, 8, 18, 38, 76, 158
6. 8, 9, 20, 63, 256, ?
7. 2, 3, 10, 15, 26, 35, ?
8. Find the wrong term: 5, 7, 12, 19, 31, 50, 83

Answers:

1. 41. Differences 2, 4, 6, 8, so next is 10.
2. 161. Each term × 2 − 1: 81 × 2 − 1.
3. 720. × 2, × 3, × 4, × 5, then × 6.
4. 60. Subtracting 4, 9, 16, 25 (squares of 2 to 5), then 36.
5. 76. The rule × 2 + 2 gives 3, 8, 18, 38, 78, 158. The series shows 76 where 78 belongs, and 78 × 2 + 2 = 158 confirms it.
6. 1,285. × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4, then 256 × 5 + 5.
7. 50. Squares plus or minus 1 in turn: 1 + 1, 4 − 1, 9 + 1, 16 − 1, 25 + 1, 36 − 1, then 49 + 1.
8. 83. Each term is the sum of the two before it: 5 + 7 = 12, 7 + 12 = 19, 12 + 19 = 31, 19 + 31 = 50, then 31 + 50 = 81, not 83.

What to do next

• Learn the standard sequences table until each row is instant.
• Do three series a day with a 90-second timer, and write which pattern each one used.
• Keep a list of patterns that fooled you. Most candidates find the same two or three catch them every time.
• See the numerical ability plan for where series fits, and the simplification guide for the calculation speed series questions need.