# Alphanumeric Series

Gaurangi Tyagi
Last Updated: Mar 10, 2023
EASY

## Introduction

Alphanumeric series is a sequence of characters containing either alphabets, numbers, or both. To solve the questions from the alphanumeric series, you need to be thorough with topics like Arithmetic Progression and Geometric progression. The questions asked from this topic are a mixed bag of coding-decoding, series-based reasoning, and position-based reasoning questions.

Alphanumeric series problems are asked in many competitive exams and the aptitude rounds of various companies. Hence, we will discuss it in detail in this blog.

Let us start by recalling the concepts of arithmetic progression and geometric progression. These concepts will help you in solving questions related to the alphanumeric series.

## Arithmetic and Geometric Progression

A.P. and G.P. are fundamental concepts in the alphanumeric series. Some essential formulas of arithmetic and geometric progression are given below.

### Arithmetic Progression

Arithmetic progression or A.P. is a series in which the difference between two consecutive terms remains constant.

#### Notations in Arithmetic Progression

In A.P., we will come across three main terms, denoted as:

• Common difference (d)

• nth Term (an)

• Sum of the first n terms (Sn)

We talk about these properties in greater detail in the next section.

#### Common Difference in Arithmetic Progression

Suppose a1, a2, a3,…,an, is an Arithmetic Progression, then; the common difference "d" can be obtained as

d = a2 – a1

d = a3 – a2 and so on.

We can generalize the formula of common difference as:

Here, "d" denotes the common difference. It can be negative, positive, or zero.

#### First Term of Arithmetic Progression

We can write the Arithmetic Progression in terms of common differences, as follows;

a, a + d, a + 2d, a + 3d, a + 4d, a+5d,…, a + (n – 1) d

Here, "a" is the first term of the progression.

#### General Form of an Arithmetic Progression

Consider an A.P.: a1, a2, a3,…, an

The general form of this A.P. will be: a + (n-1)d.

#### Formula for the nth Term of an Arithmetic Progression

The formula for finding the nth term of an A.P. is:

#### Sum of N Terms of Arithmetic Progression

We can compute the sum of the initial n terms of an Arithmetic Progression if the total number of terms and the first term are known. The formula for the sum of A.P. is given below:

Consider an A.P. consisting of “n” terms.

#### Sum of Arithmetic Progression when the Last Term is Given

The formula to find the sum of A.P. when the first and last terms are given as follows:

### Geometric Progression

A geometric progression (G.P.) is a sequence where every term contains a constant ratio to its preceding term.

#### General Form

Geometric Progression is generally of the form: a, ar, ar2, ar3, ar4,…, arn-1

[Where a is the first term, r is the common ratio, n is the number of terms, and arn-1 is the nth term].

#### nth Term

Considering the general form of the geometric progression. Then,

First term;      a1 = a

Second term; a2 = a × r

Third term;     a3 = a2 × r = ar2

Similarly;        an = arn-1

Note that the nth term is the last term of G.P.

#### Common Ratio

Considering the general form of the geometric progression.

Common ratio = (Any term) / (Preceding term)

= tn / tn-1

= (arn – 1 ) /(arn – 2)

#### Sum of n term

Considering the general form of the geometric progression.

Then the sum of n terms of G.P. is given by:

Sn = a + ar + ar2 + ar3 + ar4+…arn-1

The formula to find the sum of n terms of G.P. if the common ratio r ≠ 1 is:

Also, if the common ratio r = 1, then we can calculate the sum of the G.P. by:

## Types of problems in Alphanumeric series

Problems in alphanumeric series are majorly divided into the following three types

### Type 1

Tracking down the next term in the series
To take care of these sorts of issues, you need to notice the examples of numbers and letters in order. Begin searching for designs either from the left or right of the grouping.

#### Example

``Find the next term in the given sequence: 1,3,5,7,_``

Solution: 9

#### Explanation

Since this sequence is an A.P. with (first-term = 1 and common-difference = 2)

First term(a) = 1

Common difference(d) = (3 - 1) = 2

Tn = a + (n-1)d

Applying the formula of the nth term of A.P., we get

T= a + (n-1)*d

T= 1 + (5-1)*2

T= 9

### Type 2

Tracking down the missing term
This sort of issue is like the previous one. Here, you need to notice the example till the missing term and keep following the example up till the finish of the succession.

#### Example

``Find the missing term in the sequence: 1,4,7,_,13,16,_``

Solution: 10,19

#### Explanation

Consider the diagram given below to understand the explanation.

First term(a)=1

Common difference (d) = (7 - 4) = 3

Tn=a+(n-1)d

Substitute n with 4

T4 = 1 + (4 - 1)*3

T4=10

Substitute n with 7

T7 = 1 + (7 - 1)*3

T7=19

### Type 3

Positional inquiries
In this sort of inquiry, we will be given an arrangement and requested to discover specific letters in order or numbers dependent on a specific condition.

#### Example

``Consider a sequence in which we have to find the missing term 1, A, 4, B, 2, C, 5, D, __?``

#### Explanation

In this series, a number is followed by an alphabet and vice versa. Notice the pattern of numbers in this series. We are adding three and subtracting two alternatively. So, the missing term will be:

Missing term = (5 - 2) = 3

## Examples of Alphanumeric Series

Below are given some examples of alphanumeric series:

### Example 1

``````Find the next term of the series: 2, A, 9, B, 6, C,13, D? (Infosys Hiring 2019)

A) 9
B) 10
C) E
D) 15``````

### Solution

Let us understand the explanation of the above example with the help of the diagram below:

In this series, a number is followed by an alphabet and vice versa. Notice the pattern of numbers in this series. We are adding seven and subtracting three alternatively. So, the missing term will be:

Missing term = (13 - 3) = 10.

So, the correct option is option B.

### Example 2

Consider the sequence: ACE,? , MOQ, SUW(last term).

``````Find the term which can replace the question mark(?). (Asked in Wipro hiring ).

A) GIL
B) EHF
C) GIK
D) FHJ``````

### Solution

Let us understand the explanation of the above example with the help of the diagram below:

From the above image, we can conclude that the series moves in the given format:

(ABCDE) F (GHIJK) L (MNOPQ) R (STUVW)

You can notice that in the question, alternate alphabets are picked from this series. So the series will look like this:

ACE, GIK, MPQ, SUW

Hence, option C is correct.

Check out Infosys Interview Experience to learn about their hiring process.

### What is an alphanumeric series?

An alphanumeric series is a sequence of characters containing either alphabets, numbers, or both. In some cases, it may also include special characters like ‘@’,’&’,’*’ etc.

### What are the different types of problems on the alphanumeric series?

You may encounter three types of questions. These can be questions on finding the missing term, finding the next term, and positional inquiries.

### What is arithmetic progression?

An A.P., or arithmetic progression, is a series in which the difference b/w two consecutive terms is constant.

### What is the common difference in Arithmetic Progression?

The difference between each successive integer in an arithmetic series is a common difference.

### What is geometric progression?

A geometric progression (G.P.) is a sequence where every term contains a constant ratio to its preceding term.

## Conclusion

In this blog, we’ve covered the problem of the Alphanumeric Series and discussed how we should solve the problem of the Alphanumeric Series. You can refer to these articles to prepare for competitive exams.

You may refer to our Guided Path on Code Studios for enhancing your skill set on DSACompetitive ProgrammingSystem Design, etc. Check out essential interview questions, practice our available mock tests, look at the interview bundle for interview preparation, and so much more!
Happy Learning, Ninjas!