# Geometric sequences

3 videos

5 skills

What happens when the ratio between successive terms in a sequence is the same (or it has a "common ratio")? Well, then we'd be dealing with a geometric sequence (which comes up extremely frequently in mathematics).

### Introduction to geometric sequences

VIDEO
10:45 minutes

Sal introduces geometric sequences and their main features, the initial term and the common ratio.

### Geometric sequences

VIDEO
6:39 minutes

### Find the next term of a geometric sequence, given the first few terms

PRACTICE PROBLEMS

Solve problems such as: The first four terms of a geometric sequence are 64. -32. 16, and -8. What is the fifth term in the sequence?

### Find any term of a geometric sequence, given the formula of the sequence

PRACTICE PROBLEMS

Given a geometric sequence, ether in explicit form or in recursive form, find a specific term in the sequence.

### Find explicit formulas for geometric sequences

PRACTICE PROBLEMS

Solve problems such as: The first four terms in a geometric sequence are 1/3, 1, 3, and 9. Find an explicit formula for the sequence.

### How to convert an explicit formula of a geometric sequence to a recursive formula (example)

VIDEO
6:30 minutes

Sal solves the following problem: The explicit formula of a geometric sequence is g(x)=9*8^(x-1). Find the recursive formula of the sequence.

### Find recursive formulas for geometric sequences

PRACTICE PROBLEMS

Find the recursive formula of a geometric sequence given the first few terms or given an explicit formula. Convert a recursive formula to an explicit formula.

### Model real-world situations with arithmetic and geometric sequences

PRACTICE PROBLEMS

Given a verbal description of a real-world relationship, determine the sequence that models that relationship.