Series test

## Introduction

➡️ Questions on number series are prevalent in most of the management aptitude exams. 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.

## Different types of Number Series

1. **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.

2.

**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.

3.

**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.

4.

**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.

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.

6.

**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.

7.

**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 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.

8.

**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.