Geometric Sequences | Common Ratio & nth Term Formula | Pre-Calculus Mastery Program

Welcome back to Arun’s Math Lab 🚀

In this lesson, we explore one of the most important topics in sequences:

Geometric Sequences

A geometric sequence is a sequence where each term is obtained by multiplying the previous term by the same number.

This constant multiplier is called the common ratio.

In this video, you will learn:

✔ What is a geometric sequence
✔ How to find the common ratio
✔ Increasing and decreasing geometric patterns
✔ nth term formula
✔ Solved examples
✔ Real-life applications

📘 Formula Covered
Common Ratio

r = a₂ / a₁

nth Term Formula

aₙ = a₁ × rⁿ⁻¹

Where:

✔ aₙ = nth term
✔ a₁ = first term
✔ r = common ratio
✔ n = term number

🎯 Example Covered

2, 4, 8, 16, 32, …

Common ratio = 2

🎯 Why this topic is important

Geometric sequences help students understand:

✔ exponential growth
✔ population growth
✔ compound interest
✔ data science growth patterns
✔ future calculus concepts

This topic is extremely important for Grade 9–12 students and STEM learners.

This lesson is part of the Pre-Calculus Mastery Program, designed to build strong mathematical foundations before calculus.

📚 Best for

✔ Grade 8 students
✔ Grade 9 students
✔ Grade 10 students
✔ Grade 11 students
✔ Grade 12 students
✔ Engineering entrance preparation
✔ AI / Data Science beginners

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Видео Geometric Sequences | Common Ratio & nth Term Formula | Pre-Calculus Mastery Program канала Arun’s Math Lab