Geometric sequences

Learning Objectives Define a geometric sequence and identify its key components. Determine the common ratio of a geometric sequence. Write the formula for the nth term of a geometric sequence. Calculate any term in a geometric sequence using the formula. Distinguish between arithmetic and geometric sequences. By the end of a lesson, students will be able to model and solve real-world problems involving geometric growth or decay. Ever wonder how a single social media post can go viral, reaching millions of people in just a few hours? 📈 This explosive growth is a perfect example of a geometric sequence! In this tutorial, we'll explore geometric sequences, where you get from one term to the next by multiplying by a constant value. You'll learn how to identify these...

TermDefinitionExample SequenceAn ordered list of numbers, often following a specific pattern or rule.2, 4, 6, 8, ... is a sequence where you add 2 each time. TermEach individual number in a sequence. We use notation like a₁ for the first term, a₂ for the second term, and aₙ for the nth term.In the sequence 5, 10, 20, 40, ..., the third term (a₃) is 20. Geometric SequenceA sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number.1, 3, 9, 27, ... is a geometric sequence because you multiply by 3 each time. Common Ratio (r)The fixed number you multiply by to get from one term to the next in a geometric sequence.In the sequence 100, 50, 25, 12.5, ..., the common ratio (r) is 0.5. First Term (a₁)The starting number or the very first term in...

Finding the Common Ratio r = aₙ / aₙ₋₁ To find the common ratio (r), divide any term by the term that comes directly before it. For example, you can divide the second term by the first term (a₂ / a₁) or the third term by the second term (a₃ / a₂). The nth Term Formula aₙ = a₁ * r^(n-1) This is the general formula to find any term (aₙ) in a geometric sequence. You need the first term (a₁), the common ratio (r), and the position of the term you want to find (n).