Geometric Sequences: Identifying, Extending, Graphing, and Writing as Functions

The video tutorial covers geometric sequences, focusing on identifying them through the common ratio, classifying sequences, graphing geometric sequences, and writing equations to find specific terms. It explains the difference between arithmetic and geometric sequences, demonstrates how to graph them, and provides examples to practice identifying and extending sequences.

What is the defining characteristic of a geometric sequence?

• The terms are all prime numbers.

• The sum of terms is constant.

• The difference between terms is constant.

• The ratio between consecutive terms is constant.

In the sequence 8, 24, 72, 216, what is the common ratio?

• 2

• 5

• 4

• 3

If a sequence has a common ratio of 1/2, what type of sequence is it?

• Arithmetic

• Both

• Geometric

• Neither

Which of the following sequences is neither arithmetic nor geometric?

• 3, 6, 9, 12

• 2, 4, 8, 16

• 5, 10, 20, 40

• 2, 6, 11, 17

What is the next term in the geometric sequence 24, 48, 96?

• 144

• 120

• 192

• 72

When graphing a geometric sequence, what type of function does it form?

• Linear

• Exponential

• Quadratic

• Logarithmic

Why is a geometric sequence graph considered discrete?

• It forms a straight line.

• It has continuous values.

• It has rational values.

• It consists of distinct points.

What is the formula for finding the nth term in a geometric sequence?

• First term + (n-1) * common ratio

• First term / common ratio^(n-1)

• First term - (n-1) * common ratio

• First term * common ratio^(n-1)

Using the formula for geometric sequences, what is the 10th term if the first term is 2 and the common ratio is 6?

• 1,679,616

• 335,923

• 10,077,696

• 20,155,392

If the common ratio is negative, what can be said about the terms of the sequence?

• They will be zero.

• They will all be negative.

• They will alternate in sign.

• They will all be positive.