# Nakafa Framework: LLM

URL: /en/subject/high-school/10/mathematics/sequence-series/difference-sequence-series
Source: https://raw.githubusercontent.com/nakafaai/nakafa.com/refs/heads/main/packages/contents/subject/high-school/10/mathematics/sequence-series/difference-sequence-series/en.mdx

Output docs content for large language models.

---

export const metadata = {
  title: "Difference between Sequence and Series",
  description: "Clarify sequence vs series: ordered lists of terms vs their sums. Understand fundamental concepts with clear analogies and practical examples.",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "04/08/2025",
  subject: "Sequence and Series",
};

## Sequence

**Concept:**
A sequence is simply an **ordered list of numbers** arranged according to a specific **pattern** or rule. Each number in the list is called a **term**.

Examples:

- Sequence of even numbers: <InlineMath math="2, 4, 6, 8, \dots" />
- Sequence of squares: <InlineMath math="1, 4, 9, 16, \dots" />

The focus is on **each individual term** and how the pattern forms.

**Analogy:**
Think of a sequence like **stairs**. Each step is a term, and there's a clear order from the first step, second step, and so on.

## Series

**Concept:**
With a series, we **sum up** the terms of a sequence. So, a series is the **result of the cumulative addition** of the terms in a sequence.

Examples (using the sequences above):

- Series of even numbers: <InlineMath math="2 + 4 + 6 + 8 + \dots" />
- Series of squares: <InlineMath math="1 + 4 + 9 + 16 + \dots" />

The focus is on the **total value** or **sum** of the terms up to a certain <InlineMath math="n" />-th term (usually denoted as <InlineMath math="S_n" />).

**Analogy:**
Back to the stairs analogy. If the sequence represents the individual steps, the series represents the **total height** you've climbed after taking a certain number of steps.

## Core Difference

| Aspect      | Sequence                                                                                | Series                                                                           |
| ----------- | --------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------- |
| **Form**    | Ordered list of numbers (comma-separated) -> <InlineMath math="U_1, U_2, U_3, \dots" /> | Sum of numbers (plus-separated) -> <InlineMath math="U_1 + U_2 + U_3 + \dots" /> |
| **Focus**   | Pattern and value of each individual term                                               | Result of summing the terms                                                      |
| **Analogy** | Individual stair steps                                                                  | Total height climbed after taking stairs                                         |
