The number sequence is vital mathematical tool for experimentation a person’s intelligence. Number series problems are common in most administration aptitude exams.

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The difficulties are based upon a numerical pattern the is administrate by a reasonable rule. For example, you can be asked to predict the following number in a given collection following the to adjust rule.

The three common questions in this exam that can be asked are:

Identify a term that is wrongly placed in a given series.Find the missing number in a specific series.Complete a offered series.

What is a sequence Number?

Number succession is a development or an ordered list of numbers governed through a pattern or rule. Numbers in a sequence are dubbed terms. A succession that proceeds indefinitely there is no terminating is an unlimited sequence, whereas a sequence v an finish is known as a finite sequence.

Logic numerical difficulties generally covers one or two missing numbers and 4 or much more visible terms.

For this case, a check designer produce a succession in i beg your pardon the only one fits the number. By learning and also excising number sequence, an individual can sharpen your numerical thinking capability, which help our daily tasks such as calculating taxes, loans, or act business. For this case, the is crucial to learn and also practice number sequence.

Example 1

Which perform of numbers renders a sequence?

6, 3, 10, 14, 15, _ _ _ _ _ _4,7, 10, 13, _ _ _ _ _ _


The an initial list of number does no make a sequence because the number lack proper order or pattern.

The other list is a sequence because there is a appropriate order of obtaining the preceding number. The continually number is derived by adding 3 to the coming before integer.

Example 2

Find the absent terms in the following sequence:

8, _, 16, _, 24, 28, 32


Three continually numbers, 24, 28, and 32, are examined to uncover this sequence pattern, and also the rule obtained. Girlfriend can an alert that the corresponding number is obtained by including 4 to the preceding number.

The missing terms are therefore: 8 + 4 = 12 and 16 + 4 = 20

 Example 3

What is the worth of n in the complying with number sequence?

12, 20, n, 36, 44,


Identify the pattern of the succession by finding the difference between two continuous terms.

44 – 36 = 8 and also 20 – 12 = 8.

The sample of the succession is, therefore, the enhancement of 8 come the coming before term.


n = 20 + 8 = 28.

What room the varieties of Number Sequence?

There are numerous number sequences, yet the arithmetic sequence and geometric sequence are the most typically used ones. Let’s view them one by one.

Arithmetic Sequence

This is a type of number sequence wherein the next term is found by including a consistent value to its predecessor. When the an initial term, denoted together x1, and d is the common difference between two continually terms, the succession is generalized in the complying with formula:

xn = x1 + (n-1) d


xn is the nth term

x1 is the an initial term, n is the variety of terms and d is the usual difference in between two continuous terms.

Example 4

By taking an instance of the number sequence: 3, 8, 13, 18, 23, 28……

The common difference is found as 8 – 3 = 5;

The an initial term is 3. Because that instance, to find the fifth term making use of the arithmetic formula; substitute the worths of the first term as 3, usual difference together 5, and also the n=5

5th term =3 + (5-1) 5


Example 5

It vital to keep in mind that the common difference is not necessarily a hopeful number. There deserve to be a negative common difference as depicted in the number series below:

25, 23, 21, 19, 17, 15…….

The usual difference, in this case, is -2. We deserve to use the arithmetic formula to find any term in the series. Because that example, to obtain the 4th term.

4th term =25 + (4-1) – 2

=25 – 6


Geometric Series

The geometric collection is a number series where the adhering to or following number is obtained by multiplying the vault number by constant known as the common ratio. The geometric number collection is generalised in the formula:

xn = x1 × rn-1


x n = nth term,

x1 = the first term,

r =common ratio, and

n = number of terms.

Example 6

For example, offered a sequence favor 2, 4, 8, 16, 32, 64, 128, …, the nth term deserve to be calculate by using the geometric formula.

To calculation the 7th term, determine the first as 2, common ratio as 2 and n = 7.

7th term = 2 x 27-1

= 2 x 26

= 2 x 64

= 128

Example 7

A geometric collection can covers decreasing terms, as shown in the following example:

2187, 729, 243, 81,

In this case, the common ratio is discovered by dividing the predecessor term v the following term. This series has a usual ratio that 3.

Triangular series

This is a number series in i m sorry the very first term represents the terms attached to dots presented in the figure. Because that a triangular number, the dot shows the amount of dot compelled to fill a triangle. Triangle number collection is given by;

x n = (n2 + n) / 2.

Example 8

Take an instance of the adhering to triangular series:

1, 3, 6, 10, 15, 21………….

This pattern is created from dots the fill a triangle. It is possible to obtain a succession by including dots in an additional row and also counting all the dots.

Square series

A square number is simplifying the product of one integer with itself. Square number are constantly positive; the formula represents a square number of series

x n = n2

Example 9

Take a look in ~ the square number series; 4, 9, 16, 25, 36………. This succession repeats itself by squaring the adhering to integers: 2, 3, 4, 5, 6…….

Cube series

Cube number collection is a collection generated through the multiplication that a number 3 time by itself. The general formula because that cube number series is:

x n = n3

Fibonacci series

A mathematical series consists of a sample in i m sorry the next term is derived by including the 2 terms in-front.

Example 10

An instance of the Fibonacci number series is:

0, 1, 1, 2, 3, 5, 8, 13, …

For instance, the third term that this series is calculated as 0+1+1=2. Similarly, the 7th term is calculated as 8 + 5 = 13.

Twin series

By definition, a twin number collection comprises a mix of two series. The alternating terms the twin series can generate one more independent series.

An instance of the twin collection is 3, 4, 8, 10.13, 16, …..By closely analyzing this series, two series are created as 1, 3, 8,13 and 2, 4, 10,16.

Arithmetico-Geometric Sequence

This is a collection formed by the mix of both arithmetic and also geometric series. The distinction of consecutive state in this kind of collection generates a geometric series. Take an instance of this arithmetico -geometric sequence:

1, 2, 6, 36, 44, 440, …

Mixed Series

This form of collection is a series generated without a ideal rule.

Example 11

For example; 10, 22, 46, 94, 190, …., deserve to be addressed using the following steps:

10 x 2= 20 + 2 = 22

22 x 2 = 44 + 2 = 46

46 x 2 = 92 + 2 = 94

190 x 2 = 380 + 2 = 382

The missing term is because of this 382.

Number pattern

Number sample is typically a sequence or a sample in a collection of terms. For example, the number sample in the following collection is +5:

0, 5, 10, 15, 20, 25, 30………

In-order to solve number pattern problems, closely examine the rule governing the pattern.

Try by addition, subtraction, multiplication, or department between continuous terms.


In summary, problems involving number series and pattern call for checking the relationship in between these numbers. You should inspect for an arithmetic relationship such together subtraction and addition. Inspect for geometric relationship by dividing and multiplying the state to uncover their usual ratio.

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Practice Questions

Find the absent number R in the collection below:7055, 7223, 7393, 7565, R, 7915,Which ax in the following collection is wrong38, 49, 62, 72, 77, 91, 101,Find out the dorn number in the adhering to series7, 27, 93, 301, 915, 2775, 8361What is the absent number in the location of question note (?)4, 18, 60, 186, 564, ?Find the absent term in the complying with b series:2184, 2730, 3360, 4080, 4896, ?, 6840Calculate the absent number in the following series:2, 1, (1/2), (1/4)Find the lacking term x in the collection given below.1, 4, 9, 16, 25, xIdentify the lacking number or number in the complying with seriesa. 4, ?, 12, 20, ?b. ?, 19, 23, 29, 31c. , 49, ?, 39, 34d. 4, 8, 16, 32, ?Previous Lesson | Main web page | following Lesson