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Table of contents
1.
Introduction
2.
Sequence
3.
Series
4.
Differences
5.
FAQs
6.
Key Takeaways
Last Updated: Mar 27, 2024
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Difference Between Sequence and Series

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Introduction

Sequence and Series are the two most confusing words in the mathematics world. Most of the time, Sequence and Series are considered identical. But, they are not the same. This article will briefly discuss Sequence and Series and discuss the critical differences between Sequence and Series.

Sequence

It is a collection of numbers arranged in a specific order. The terms in a sequence can be repeated multiple times, but they need to follow some order or pattern. 

Some examples of Sequence are given below:

  1. 1, 2, 3, 4, 5, 6
    Here every term is one greater than the previous term. So, it follows a pattern.
  2. 0, 5, 10, 15, 20
    Here every term is five greater than the previous term.
  3. 1, 10, 100, 1000
    Here every term is ten times the previous term.

Sequences can be of two types:

  1. Finite Sequence: The number of terms is fixed and a limited number. All the examples discussed above were of a finite sequence.
  2. Infinite Sequence: The number of terms is infinite. Example: 1, 2, 3, 4, . . .

The Sequence can be represented as

 where an is a term of the Sequence ranging from 1 to infinity.

Some types of Sequence are:

  • Arithmetic Sequence
  • Geometric Sequence
  • Harmonic Sequence
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Series

A series can be defined as the sum of the terms in a sequence. The terms of a series may or may not follow an order for a straightforward reason as a+b+c = b+a+c. Series, in general, is of the form

a1 + a2 + a3 + a4 + . . . + an

It is nothing but the sum of the Sequence. Series can be finite or infinite depending on the Series if it is finite or infinite.

If [a1, a2, a3, a4, a5] is a sequence then [a1+a2+a3+a4+a5] is a series. A series can be represented as

Some common types of series are:

  • Alternating Series
  • Harmonic Series
  • Exponential Series

Now, let's discuss the differences between Sequence and Series.

Differences

Check out this problem - Shortest Common Supersequence

FAQs

  1. What is a sequence?
    A sequence is a group of numbers arranged in a specific pattern or order.
  2. What is a series?
    Series is the sum of the terms in a sequence.
  3. What is progression?
    A progression is a group of numbers following a pattern where a mathematical formula can find a term at any position.
  4. What is the difference between a sequence and a progression?
    A group of prime numbers is a sequence but not a progression since it follows a logical but not mathematical pattern. All progressions are a sequence, but all sequences are not a progression.
  5. What is a geometric sequence?
    Every term is a multiplication of a constant number and its predecessor in a geometric sequence. Example: 2, 4, 8, 16. Here every term is two times its previous term.

Key Takeaways

In this article, we have extensively discussed the differences between Sequence and Series. We hope that this blog has helped you enhance your engineering mathematics and series knowledge. If you would like to learn more, check out our other articles.

  1. Sequence and Series
  2. Arithmetic Progression
  3. Harmonic Progression
  4. Mean, Variance, and Standard Deviation
  5. Initial Value Theorem
  6. IEnumerable vs IQueryable

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