Number series (missing and wrong) for IBPS PO

Number series look intimidating because the numbers jump around. In practice, bank exam series are built from a small family of patterns, and a candidate who checks them in a fixed order finds most answers in about 20 seconds. The candidate who stares at the numbers hoping to "see" the pattern takes a minute, and sometimes never sees it.

This guide gives you that fixed order, explains why it works, and shows it on the patterns that come up again and again in IBPS PO.

How series questions are asked

• Missing term: five or six terms and a "?", usually at the end, sometimes in the middle. Find the missing number.
• Wrong term: a complete series in which one number breaks the pattern. Find it.
• Both types have often appeared as a set of about five in the prelims. The mains occasionally uses harder series, sometimes combined with other questions. Always read the instruction: a wrong-term question asks you to pick a term from the series, not to calculate a new one.

The checking routine

1. Look at the growth. Slow, steady growth suggests differences. Growth that doubles or triples suggests multiplication. Terms that shrink suggest division or subtraction.
2. Differences. Write the gaps between terms. Are they constant, squares (1, 4, 9, 16…), cubes (1, 8, 27, 64…), doubling, or a simple series of their own?
3. Ratios. If each term is roughly 2×, 3× or 4× the one before, look for × n + k: a multiplier that is fixed or rising, plus a small number that is fixed or rising.
4. Division by rising numbers. Shrinking terms often follow ÷2, ÷3, ÷4…
5. Squares and cubes. Compare each term with the nearest square or cube: is it n² ± something, n³ ± something?
6. Two series mixed. If nothing fits, check odd and even positions separately, or alternating operations (×2, then −3, and so on).

Why this order works: a series built by adding grows roughly in a straight line or a gentle curve, while a series built by multiplying grows exponentially. Looking at growth first tells you which half of the routine to use, so you rarely try more than two or three checks.

Worked examples: missing term

Example 1: 12, 13, 17, 26, 42, ?

• Differences: 1, 4, 9, 16. These are squares.
• Next difference: 25. Answer: 42 + 25 = 67.

Example 2: 5, 11, 35, 143, ?

• The terms roughly double, then triple, then quadruple. Test × n + k.
• 5 × 2 + 1 = 11; 11 × 3 + 2 = 35; 35 × 4 + 3 = 143.
• Next: 143 × 5 + 4 = 719.

Example 3: 720, 360, 120, 30, 6, ?

• Shrinking fast: test division. ÷2, ÷3, ÷4, ÷5.
• Next: 6 ÷ 6 = 1.

Example 4: 64, 32, 48, 120, 420, ?

• The terms first fall, then rise faster. Test ratios: 32/64 = 0.5; 48/32 = 1.5; 120/48 = 2.5; 420/120 = 3.5.
• Multipliers rise by 1: next is × 4.5.
• Answer: 420 × 4.5 = 1,890.

Example 5: 2, 3, 11, 38, 102, ?

• Differences: 1, 8, 27, 64. These are cubes.
• Next difference: 125. Answer: 102 + 125 = 227.

Worked examples: wrong term

Example 6: 3, 5, 9, 17, 35, 65

• Test × 2 − 1: 3 → 5 → 9 → 17 → 33 → 65.
• Every term fits except 35. The wrong term is 35.

Example 7: 2, 8, 26, 80, 244, 728

• Test × 3 + 2: 2 → 8 → 26 → 80 → 242 → 728.
• Note that 242 × 3 + 2 = 728, so the last term confirms the rule. The wrong term is 244.

Other patterns to know

The last row needs a word. The differences are 1, 3, 6, 11, which look random. Their own differences are 2, 3, 5: prime numbers. The next prime is 7, so the next difference is 11 + 7 = 18, and 24 + 18 = 42. When the first differences look random, always check their differences before giving up.

Speed habits

• Know squares to 30 and cubes to 15 by sight. Most series hide them.
• Write the differences under the series on your rough sheet; do not hold them in your head.
• Stop at four terms. Once a rule fits four terms, calculate the answer. Testing all six wastes time in a missing-term question, but is essential in a wrong-term one.
• Skip after 40 seconds. If none of the six checks has worked, mark it and move on.

Practice set

1. 4, 6, 10, 18, 34, ?
2. 2, 3, 8, 27, 112, ?
3. 1,440, 720, 240, 60, 12, ?
4. Find the wrong term: 7, 12, 22, 42, 81, 162
5. 1, 4, 13, 40, 121, ?
6. 120, 99, 80, 63, 48, ?
7. 1, 2, 6, 15, 31, ?
8. Find the wrong term: 1, 3, 10, 42, 206, 1,237

Answers:

1. 66. Differences 2, 4, 8, 16 double each time; next is 32.
2. 565. × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4; next 112 × 5 + 5.
3. 2. ÷2, ÷3, ÷4, ÷5; next 12 ÷ 6.
4. 81. The rule is × 2 − 2: 42 × 2 − 2 = 82, and 82 × 2 − 2 = 162 confirms it.
5. 364. × 3 + 1: 121 × 3 + 1.
6. 35. The terms are 11² − 1, 10² − 1, 9² − 1, 8² − 1, 7² − 1, so next is 6² − 1. The differences (−21, −19, −17, −15, then −13) give the same answer.
7. 56. Differences 1, 4, 9, 16 are squares; next is 25.
8. 42. The rule is × n + 1 with n rising: 1 × 2 + 1 = 3; 3 × 3 + 1 = 10; 10 × 4 + 1 = 41, not 42; then 41 × 5 + 1 = 206 and 206 × 6 + 1 = 1,237 confirm it.

What to do next

• Learn squares to 30 and cubes to 15 until you recognise them on sight.
• Do ten series a day for two weeks, writing the routine step you used for each.
• Take one timed set of five every other day, aiming for under two minutes.
• Pair series with the other fast blocks: simplification and quadratic equations. The full picture is in the quant plan.