Concept:
Generally, you are given a series having some numbers and a missing number.
Finding that number is sometimes easy if the series contains the multiples of the same number or based on simple addition or subtraction, but sometimes there is a pattern you need to find out to identify the missing number.
Missing Number Series Tricks:
To find out the missing number, you need to identify the pattern between the given series.
Check that the series is only increasing/ decreasing or both. Then check the difference between 2 numbers, all these will help you to find the pattern.
If you can’t see any pattern, there are few common patterns that are widely used in these type of questions like:
Common Number Series Patterns
Perfect Squares: 196, 225, 256, 289, 324
Perfect Cubes: 343, 512, 729, 1000
Geometric Series: 7, 21, 63, 189
Arithmetic Series: 17, 21, 25, 29, 33
Increasing Difference: 2, 5, 9, 14, 20
Types of Missing Number Problems and Tricks
Equation-Based Problem
Example: 10, 22, 46, 94, 190, ?
Solution: You can see that the numbers are always increasing, hence there will be a case of addition or multiplication. We also notice that next number is somewhat greater than twice the previous number.
Hence the pattern can be: 2x + 2 for the next number
Increasing alternate difference
Example: 3, 4, 8, 10, 13, 16, 18, ?
Solution: You can see that the numbers are always increasing, hence there will be a case of addition or multiplication. Let’s just see the difference between every term.
Taking alternative terms,
3, 4 i.e. 3 + 1
8, 10 i.e. 8 +2
13, 16 i.e. 13 + 3
Remaining alternative terms,
4, 8 i.e. 4 + 4
10, 13 i.e. 10 + 3
16, 18 i.e. 16 + 2
Explanation:
You can notice that alternatively the difference is increasing and simultaneously decreasing for next alternative terms. Hence the next term would be 18 + 4 i.e. 22
Square or cubes
Example: 1, 8, 9, 64, 25, 216, ?
Solution: Here the numbers are increasing and decreasing both, hence subtraction / division can also be presented.
Here, you can see that every number is either square or cube of some number. Hence just write down their possibilities.
12 or 13, 23, 32, 82 or 43, 52, 63
Here we can notice that terms are in the order of being square of first number, then cube of the next.
Hence the series can be written as,
12, 23, 32, 43, 52, 63, 72 i.e. 49
Example: 1, 2, 6, 24, ?
Solution: Here, the numbers are increasing with large margins, hence it is possible that there can be multiplication.
We can write the series as: 1×1, 1×2, 2×3 and 6×4
Here, we can notice that the equation can be (previous term x n) where n is incrementing by 1.
Hence the next term can be 24×5 i.e. 120
This article is contributed by Shushank Mittal.