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# 2. Basics of Number Series

The arrangement of numbers in a certain order, and in which some numbers are placed wrongly in the series and some numbers are missing is called a number series.

Based on calculating the addition and subtraction of the numbers, candidates have to observe and find the accurate number to the series of numbers.

Steps to solve Number Series

Here we are providing some steps on how to solve number series question that forms an important part of the reasoning section of the banking syllabus:

Step 1: Screening

Candidates should first read the question carefully. Sometimes reading the question carefully can be enough for the candidate to solve the question.

Example:

1, 3, 7, 13, 21, 21, 31, ?

In this series, the terms are increasing by +2, +4, +6, +8, +10. So, the next term will be increased by 12. Hence, the next term is 31 + 12 = 43.

2, 4, 8, 16, 32, 64, ?

In this series, the terms are increasing by the multiples of 2. Therefore, the next term will be 64 * 2 = 128.

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Step 2: Check the pattern Decreasing or Increasing or Alternating.

Sometimes candidates fail to decipher the pattern of the number series. During bank exam preparation, candidates should try to find out the trend of the series by looking at the series pattern. They can find it by checking the series whether it is decreasing or increasing or it is following an alternate pattern.

Example:

5, 10, 13, 26, 29, 58

Clearly, we can see that it is an increasing pattern.

729, 512, 343, 216, 125

Here, we can see that the series is of decreasing pattern.

4, -8, 16, -32, 64, -128

This series is neither increasing nor decreasing. So clearly, it is following an alternating pattern.

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Step 3: Find the rate of increase or decrease if the series is of increasing or decreasing pattern.

During bank exam preparation, candidates should read the question carefully and find whether the nature of the series is increasing or decreasing. Moreover, on the basis of that, they should find the rate at which the terms are increasing or decreasing.

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Here are some of the series patterns which are discussed below:

• Based on subtraction and addition

In the series 4, 9, 14, 19, 24, 29 we can see that it is an increasing series and the rate of increase is 9-4 = 5.

In the series 13, 11, 9, 7, 5 we can see that it is a decreasing series and the rate of decrease is 13-11 = 2

• Based on division and multiplication

In the series 4, 8, 16, 32, 64, we can see that it is an increasing series and the series is increasing by the multiple of 2.

In the series 100, 50, 25, 5, 1 we can see that it is a decreasing series and the series is decreasing as the terms are divided by 5.

• Based on square and cube

In the series 8, 27, 125, 343, 1331, 2197, we can see that it is an increasing series. The series is the cube of the consecutive prime numbers from 2 to 13.

Step 4: Check if the series is alternating

For alternating series, candidates need to check whether the series has two different operations, which are being alternately performed, or there is a mix of two series.

Example:

In the series 4, 9 6, 18, 9, 27, 13, 36. This series is a mix of two series 9, 18, 27, 36 and 4, 6, 9, 13.

In the series 200, 600, 1200, 1600, 3200, 3600, 7200 two types of operations are going, one is the addition of 400 and the second is multiplication by 2.