Geometric Sequences

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Dive into the fascinating world of geometric sequences in Chapter 5, Lesson 6. This lesson explores the fundamental characteristics of geometric sequences, including the common ratio and recursive formulas. Learn how to apply the NEXT-NOW method to predict future terms in a sequence and formulate explicit equations. Through various examples, we’ll address how to write recursive formulas for given terms and solve problems involving geometric sequences as functions. Enhance your skills in recognizing patterns and solving complex mathematical problems.

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Jun 08, 2026

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Geometric Sequences

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Geometric Sequences Chapter 5 – Lesson 6
With a partner …
What is it? • Geometric sequence – a set of terms that has a common ratio • EX 1, 8, 64, 512, … • EX2 -4, 8, -16, 32, …
NEXT-NOW Statements • Uses NEXT = NOW * r (r=common ratio) • EX 1, 4, 16, 64, … • EX2 -2, 4, -8, 16, … • EX3
Recursive Formula • for n ≥ 2 • EX 1, 4, 16, 64, … • EX2 2, -4, 8, -16, …
Try a couple … • Write a NEXT-NOW statement and a recursive formula for each sequence. Then, find the next three terms. • 1) 1/3, 1/9, 1/27, 1/81, … • 2) 5, 25, 125, 625, …
Explicit Formula • for n ≥ 1 • EX 1, 4, 16, 64, … • EX2 2, -4, 8, -16, …
Problem Solving
Geometric Sequences as Functions • Write as an exponential equation …