The number sequence is an important mathematical tool for testing a who intelligence. Number series problems are common in most management aptitude exams.

You are watching: The number which best completes the sequence below is: 10 8 7 14 15 13 12 24 25

The problems are based upon a numerical pattern the is administrate by a reasonable rule. Because that example, you might be asked come predict the following number in a given collection following the set rule.

The three widespread questions in this exam that have the right to be asked are:

Identify a term that is wrongly inserted 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 progression or one ordered list of numbers governed through a pattern or rule. Number in a sequence are referred to as terms. A sequence that continues indefinitely there is no terminating is an unlimited sequence, vice versa, a sequence v an end is known as a limited sequence.

Logic numerical troubles generally covers one or two lacking numbers and also 4 or much more visible terms.

For this case, a check designer produce a sequence in i m sorry the only one fits the number. By learning and also excising number sequence, an individual deserve to sharpen their numerical reasoning capability, which help our daily activities such together calculating taxes, loans, or law business. For this case, that is important to learn and practice number sequence.

Example 1

Which list of numbers renders a sequence?

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

Solution

The very first list of numbers does no make a sequence due to the fact that the number lack appropriate order or pattern.

The various other list is a sequence since there is a proper order of obtaining the preceding number. The consecutive number is obtained by adding 3 come the preceding integer.

Example 2

Find the absent terms in the adhering to sequence:

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

Solution

Three continuous numbers, 24, 28, and 32, space examined to uncover this succession pattern, and the rule obtained. You can notice that the corresponding number is acquired by including 4 come the preceding number.

The lacking terms space therefore: 8 + 4 = 12 and also 16 + 4 = 20

Example 3

What is the value of n in the following number sequence?

12, 20, n, 36, 44,

Solution

Identify the sample of the succession by finding the difference in between two consecutive terms.

44 – 36 = 8 and also 20 – 12 = 8.

The pattern of the sequence is, therefore, the enhancement of 8 come the preceding term.

So,

n = 20 + 8 = 28.

## What room the varieties of Number Sequence?

There are countless number sequences, however the arithmetic sequence and also geometric sequence are the most generally used ones. Let’s view them one through one.

### Arithmetic Sequence

This is a form of number sequence where the next term is discovered by including a consistent value to its predecessor. Once the first term, denoted together x1, and also d is the typical difference between two consecutive terms, the succession is generalized in the following formula:

xn = x1 + (n-1) d

where;

xn is the nth term

x1 is the first term, n is the number of terms and d is the common difference in between two continuous terms.

Example 4

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

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

The first term is 3. For instance, to uncover the fifth term making use of the arithmetic formula; substitute the values of the very first term together 3, common difference as 5, and also the n=5

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

=23

Example 5

It necessary to keep in mind that the common difference is not necessarily a hopeful number. There deserve to be a an adverse common difference as shown in the number series below:

25, 23, 21, 19, 17, 15…….

The typical difference, in this case, is -2. We can use the arithmetic formula to find any type of term in the series. For example, to obtain the fourth term.

4th ax =25 + (4-1) – 2

=25 – 6

=19

### Geometric Series

The geometric collection is a number series where the following or following number is derived by multiplying the ahead number by continuous known together the usual ratio. The geometric number collection is generalized in the formula:

xn = x1 × rn-1

where;

x n = nth term,

x1 = the an initial term,

r =common ratio, and

n = variety of terms.

Example 6

For example, provided a sequence choose 2, 4, 8, 16, 32, 64, 128, …, the nth term can be calculated by using the geometric formula.

To calculate the 7th term, recognize the very first as 2, usual ratio together 2 and also n = 7.

7th hatchet = 2 x 27-1

= 2 x 26

= 2 x 64

= 128

Example 7

A geometric collection can covers decreasing terms, as presented in the adhering to example:

2187, 729, 243, 81,

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

### Triangular series

This is a number collection in which the an initial term represents the terms connected to dots presented in the figure. Because that a triangle number, the dot reflects the quantity of dot forced to fill a triangle. Triangular number series is offered 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 produced from dots that fill a triangle. The is feasible to acquire a succession by including dots in one more row and counting every the dots.

### Square series

A square number is simple the product of an integer v itself. Square number are constantly positive; the formula to represent a square variety of series

x n = n2

Example 9

Take a look at the square number series; 4, 9, 16, 25, 36………. This sequence repeats itself by squaring the complying with integers: 2, 3, 4, 5, 6…….

### Cube series

Cube number series is a series generated by the multiplication the a number 3 time by itself. The basic formula for cube number series is:

x n = n3

### Fibonacci series

A mathematical series consists the a sample in i beg your pardon the following term is acquired by adding the 2 terms in-front.

Example 10

An instance of the Fibonacci number collection is:

0, 1, 1, 2, 3, 5, 8, 13, …

For instance, the 3rd term the this collection is calculated as 0+1+1=2. Similarly, the 7th ax is calculated as 8 + 5 = 13.

### Twin series

By definition, a pair number collection comprises a combination of 2 series. The alternate terms of twin collection can generate an additional independent series.

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

### Arithmetico-Geometric Sequence

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

Example 11

For example; 10, 22, 46, 94, 190, …., can be resolved using the complying with 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 pattern is usually a succession or a sample in a collection of terms. Because that example, the number sample in the following series is +5:

0, 5, 10, 15, 20, 25, 30………

In-order to solve number pattern problems, closely check the dominance governing the pattern.

Try through addition, subtraction, multiplication, or department between consecutive terms.

## Conclusion

In summary, troubles involving number series and pattern require checking the relationship between these numbers. Friend should examine for one arithmetic connection such as subtraction and also addition. Inspect for geometric relationship by dividing and also multiplying the terms to find their common ratio.

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### Practice Questions

Find the absent number R in the collection below:7055, 7223, 7393, 7565, R, 7915,Which hatchet in the following series is wrong38, 49, 62, 72, 77, 91, 101,Find the end the not correct number in the complying with series7, 27, 93, 301, 915, 2775, 8361What is the lacking number in the place of question mark (?)4, 18, 60, 186, 564, ?Find the missing term in the following b series:2184, 2730, 3360, 4080, 4896, ?, 6840Calculate the missing number in the following series:2, 1, (1/2), (1/4)Find the absent term x in the series given below.1, 4, 9, 16, 25, xIdentify the missing number or numbers in the following seriesa. 4, ?, 12, 20, ?b. ?, 19, 23, 29, 31c. , 49, ?, 39, 34d. 4, 8, 16, 32, ?Previous Lesson | Main page | following Lesson