What the exam asks
SBI Clerk Prelims usually has 5 missing number questions (find ?). Mains may ask wrong number questions (one term breaks the pattern). Target: 30 seconds per question.
The 30-second checking order
- Look at growth. Slow growth suggests addition/subtraction; fast growth suggests multiplication; very fast growth suggests x n + n type or powers.
- First differences. Write the gaps. If they form a pattern (constant, AP, squares, primes, doubling), you are done.
- Second differences if first differences are irregular.
- Ratios (x1.5, x2, x2.5 ...) when terms multiply.
- Mixed operations: x 2 + 1, x 3 - 2, x n + n, x n - n², etc.
- Alternate series: two series interleaved (check 1st, 3rd, 5th and 2nd, 4th, 6th separately).
Common pattern types
| Type | Example | Rule |
|---|---|---|
| Difference AP | 5, 8, 14, 23, 35 | +3, +6, +9, +12 |
| Squares / cubes | 2, 6, 15, 31, 56 | +2², +3², +4², +5² |
| Primes | 5, 10, 17, 28, 41 | +5, +7, +11, +13 |
| Doubling gaps | 7, 11, 19, 35, 67 | +4, +8, +16, +32 |
| Multiplier AP | 4, 6, 12, 30, 90 | x1.5, x2, x2.5, x3 |
| x n + n | 3, 4, 10, 33, 136 | x1+1, x2+2, x3+3, x4+4 |
| x 2 + 1 | 3, 7, 15, 31, 63 | each term = 2 x previous + 1 |
| n² ± 1, n³ ± 1 | 3, 8, 15, 24, 35 | 2² - 1, 3² - 1, 4² - 1 ... |
Worked example (missing number)
3, 4, 10, 33, 136, ?
Growth is very fast, so test multiply-and-add: 3 x 1 + 1 = 4, 4 x 2 + 2 = 10, 10 x 3 + 3 = 33, 33 x 4 + 4 = 136. Next = 136 x 5 + 5 = 685.
Worked example (wrong number)
7, 11, 19, 35, 66, 131
Gaps: 4, 8, 16, 31, 65. The doubling pattern needs 4, 8, 16, 32, 64, so the term after 35 should be 67. The wrong number is 66. Check the next term too: 67 + 64 = 131 fits.
Wrong-number trick: find the pattern from the first three or four terms and the last two terms; the odd term is usually in the middle. Always confirm by checking that the corrected value makes the next gap work too.
Useful lists to memorise
- Primes up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
- Powers of 2 up to 2^12 = 4,096 and powers of 3 up to 3^7 = 2,187.
- Squares up to 30 and cubes up to 20 (see Simplification notes).
Common traps
- Stopping at the first difference that "looks" right; verify it across every term.
- Missing an alternate series: 2, 10, 4, 20, 8, 40 is two series (2, 4, 8) and (10, 20, 40).
- In wrong-number questions, correcting the wrong term changes the next difference - check both sides.
Time target: 30 seconds each. If no pattern appears in 45 seconds, skip and return later.