Derivation of the Arithmetic Series Formula

📘 Derivation of the Arithmetic Series Formula | Grade 10–12 Mathematics Tutorial
In this lesson, we walk step by step through the derivation of the arithmetic series formula, helping learners understand where the formula comes from rather than just memorising it.
This tutorial is ideal for high school Mathematics learners (Grades 10–12) following CAPS or IEB, and for anyone who wants to build a strong conceptual foundation in sequences and series.
🔍 What you’ll learn in this video:


What an arithmetic sequence is


The meaning of an arithmetic series


How to write the series using first and last terms


A clear, logical derivation of the formula
Sn=n2(a+l)S_n = \frac{n}{2}(a + l)Sn​=2n​(a+l)


How the alternative form
Sn=n2(2a+(n−1)d)S_n = \frac{n}{2}\big(2a + (n - 1)d\big)Sn​=2n​(2a+(n−1)d)
is obtained


Why this formula always works


✏️ Why this video is important:
Many learners struggle with series because they memorise formulas without understanding them. This lesson focuses on reasoning, patterns, and mathematical thinking, which are essential for tests and exams.
📌 Perfect for:


Grade 10, 11, and 12 Mathematics


CAPS & IEB curriculum


Exam preparation and revision


Learners who want clarity and confidence in sequences and series


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