Geometric Sequences and Functions

This video tutorial covers the identification, extension, and graphing of geometric sequences. It explains how to determine if a sequence is arithmetic, geometric, or neither, and how to find the next terms in a geometric sequence. The tutorial also demonstrates how to graph geometric sequences, showing their exponential nature, and how to express them as functions. Finally, it applies these concepts to solve real-world problems, such as determining the number of zoom-out clicks needed to reach a specific map size.

What is a geometric sequence?

• A sequence where each term is the sum of the previous term and a constant.

• A sequence where each term is the product of the previous term and a constant.

• A sequence where each term is the difference of the previous term and a constant.

• A sequence where each term is the quotient of the previous term and a constant.

In a geometric sequence, what is the common ratio?

• The sum of consecutive terms.

• The product of consecutive terms.

• The ratio between consecutive terms.

• The difference between consecutive terms.

How do you determine if a sequence is geometric?

• Check if the difference between terms is constant.

• Check if the ratio between terms is constant.

• Check if the sum of terms is constant.

• Check if the product of terms is constant.

What is the common ratio in the sequence 120, 60, 30, 15?

• 1/2

• 2

• 1/3

• 3

Why is the sequence 2, 6, 11, 17 neither arithmetic nor geometric?

• The difference between terms is not constant.

• The ratio between terms is not constant.

• Both the difference and ratio between terms are not constant.

• The sequence is arithmetic.

What is the next term in the sequence 3, 6, 12, 24?

• 72

• 96

• 48

• 36

What is the common ratio in the sequence 64, -16, 4, -1?

• -1/4

• 1/4

• -4

• 4

What type of curve does a geometric sequence form when graphed?

• Exponential

• Linear

• Logarithmic

• Quadratic

What happens to the terms of a geometric sequence as they approach zero?

• They never reach zero.

• They oscillate.

• They become negative.

• They reach zero.

How can you express a geometric sequence as a function?

• Using an exponential function.

• Using a quadratic equation.

• Using a linear equation.

• Using a logarithmic function.