# Number series : Logical Reasoning

Updated: Aug 24

Series logical reasoning and number series reasoning tricks

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These questions are based on numerical sequences that follow a logical rule/ pattern based on elementary arithmetic concepts. A particular series is given from which the pattern must be analyzed. You are then asked to predict the next number in the sequence following the same rule.

Generally, there are three types of questions asked from the number series: A numerical series is given in which a number is wrongly placed. You are asked to identify that particular wrong number.

A numerical series is given in which a specific number is missing. You are required to find out that missing number. A complete numerical series is followed by an incomplete numerical series. You need to solve that incomplete numerical series in the same pattern in which the complete numerical series is given.

**Different types of Number Series:**
The most common patterns followed by number series are:

**Series consisting of Perfect Squares:**
A series based on Perfect squares is most of the times based on the perfect squares of the numbers in a specific order & generally one of the numbers is missing in this type of series.

*Example:324, 361, 400, 441,?*
Sol: 324 = 182 , 361 = 192, 400 = 202, 441 = 212, 484 = 222

**Perfect Cube Series:**
It is based on the cubes of numbers in a particular order and one of the numbers is missing in the series.

*Example:512, 729, 1000,?*
Sol:83, 93, 103, 113

**Geometric Series:**
It is based on either descending or ascending order of numbers and each successive number is obtained by dividing or multiplying the previous number by a specific number.

*Example:4, 36, 324, 2916?*
Sol:4 x 9 = 36, 36 x 9 = 324, 324 x 9 = 2916, 2916 x 9 = 26244.

**Arithmetic Series:**
It consists of a series in which the next term is obtained by adding/subtracting a constant number to its previous term.

*Example: 4, 9, 14, 19, 24, 29, 34 in which the number to be added to get the new number* is 5.

Now, we get an arithmetic sequence 2,3,4,5.

**Two-stage Type Series:**
In a two step Arithmetic series, the differences of consecutive numbers themselves form an arithmetic series.

*Example: 1, 3, 6, 10, 15.....*
Sol:3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4, 15 - 10 = 5....
Now, we get an arithmetic sequence 2, 3, 4, 5

**Mixed Series:**
This particular type of series may have more than one pattern arranged in a single series or it may have been created according to any of the unorthodox rules.

*Example:10, 22, 46, 94, 190,?*
Sol:
10 x 2 = 20 +2 = 22,
22 x 2 = 44 + 2 = 46,
46 x 2 = 92 + 2 = 94,
94 x 2 = 188 + 2 = 190,
190 x 2 = 380 + 2 = 382.
So the missing number is 382.

**Arithmetico –Geometric Series :**
As the name suggests, Arithmetico –Geometric series is formed by a peculiar combination of Arithmetic and Geometric series. An important property of Arithmetico- Geometric series is that the differences of consecutive terms are in Geometric Sequence.

*Example:1, 4, 8, 11, 22, 25, ?*
Sol :Series Type +3 , X2 ( i.e Arithmetic and Geometric Mixing)
1 + 3 = 4, 4 X 2 = 8, 8 + 3 = 11, 11 X 2 = 22, 22 + 3 = 25, 25 X 2 = 50

**Geometrico - Arithmetic Series**

This is the reverse of Arithmetico - Geometric Series. The differences of suggestive terms are in Arithmetic Series.

*Example: 1, 2, 6, 36, 44, 440, ?*
Sol :Series Type - X 2, + 4, X 6, +8 , X 10
1 X 2 = 2, 2 + 4 = 6, 6 X 6 = 36, 36+ 8 = 44, 44 X 10 = 440, 440 + 12 = 452

**Twin/Alternate Series :**
As the name of the series specifies, this type of series may consist of two series combined into a single series. The alternating terms of this series may form an independent series in itself.

*Example: 3, 4, 8, 10, 13, 16 ? ?*
Sol: As we can see, there are two series formed

Series 1 : 3, 8, 13 with a common difference of 5 Series 2 : 4, 10, 16 with a common difference of 6

So, next two terms of the series should be 18 & 22 respectively.