# Alphanumeric Series

**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)**

**n**^{th}Term (a_{n}**)**

**Sum of the first n terms (S**_{n}**)**

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

**Common Difference in Arithmetic Progression**

Suppose a_{1}, a_{2}, a_{3,…,}a_{n}, is an Arithmetic Progression, then; the common difference "d" can be obtained as

d = a_{2} – a_{1}

d = a_{3} – a_{2} and so on.

We can generalize the formula of common difference as:

d = a_{n} – a_{n-1} |

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.: a_{1}, a_{2}, a_{3},…, a_{n}.

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

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 n^{th} term of an A.P. is:

a_{n} = a + (n − 1) × d |

**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.

S_{n} = n/2[2a + (n − 1) × d] |

**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:

S_{n} = n/2 (first term + last term) |

**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, ar ^{2}, ar^{3}, ar^{4},…, ar^{n-1}**

[Where a is the first term, r is the common ratio, n is the number of terms, and ar^{n-1} is the n^{th} term].

**n**^{th} Term

^{th}Term

Considering the general form of the geometric progression. Then,

First term; a_{1} = a

Second term; a_{2} = a × r

Third term; a_{3} = a_{2} × r = ar^{2}

Similarly; a_{n} = ar^{n-1}

n^{th} term → a_{n} = ar^{n-1} |

Note that** **the** **n^{th} term is the last term of G.P.

**Common Ratio**

Considering the general form of the geometric progression.

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

= t_{n} / t_{n-1}

= (ar^{n – 1 }) /(ar^{n – 2})

Common ratio = r |

**Sum of n term**

Considering the general form of the geometric progression.

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

**S _{n} = a + ar + ar^{2} + ar^{3} + ar^{4}+…ar^{n-1}**

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

S_{n} = a[(r^{n}-1)/(r-1)] |

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

S_{n} = n*a |

**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

T_{n} = a + (n-1)d

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

T_{5 }= a + (n-1)*d

T_{5 }= 1 + (5-1)*2

**T _{5 }= 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

T_{n}=a+(n-1)d

Substitute n with 4

T_{4} = 1 + (4 - 1)*3

**T _{4}=10**

Substitute n with 7

T_{7} = 1 + (7 - 1)*3

**T _{7}=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, __?`

**Answer:** 3

**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

Thus, the** answer is GIK**.

Hence, **option C** is correct.

Check out __Infosys Interview Experience__ to learn about their hiring process.

Let us now answer some frequently asked questions.

**Frequently Asked Questions**

**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.

__Percentages____Dice____General A.P.titude____How to crack the A.P.titude test____Important Aptitude topics for placements__

You may refer to our __Guided Path__ on __Code Studios__ for enhancing your skill set on __DSA__, __Competitive Programming__, __System 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!