Geometric Sequences and Their Properties

The video tutorial explains how to find the 12th term of two geometric sequences by determining the common ratio and using the geometric sequence formula. The first sequence has a common ratio of -2, leading to a 12th term of -8,192. The second sequence has a common ratio of 1/2, resulting in a 12th term of 25/1,224. The tutorial demonstrates the use of a calculator for these calculations and emphasizes the importance of exact values over decimal approximations.

What is a common characteristic of geometric sequences?

• They have a variable ratio.

• They have a common difference.

• They have a common ratio.

• They have a constant sum.

How do you calculate the common ratio in a geometric sequence?

• By dividing any term by its previous term.

• By dividing the first term by the second term.

• By adding the first two terms.

• By subtracting the first term from the second term.

What is the common ratio of the first sequence if the first term is 4 and the second term is -8?

• 2

• -2

• 4

• -4

Using the formula A_n = A_1 * r^(n-1), what is the 12th term of the first sequence where A_1 = 4 and r = -2?

• -4096

• 8192

• -8192

• 4096

What is the first term of the second sequence?

• 50

• 75

• 25

• 100

What is the common ratio of the second sequence if the first term is 50 and the second term is 25?

• 2

• 1/4

• 1/3

• 1/2

Using the formula A_n = A_1 * r^(n-1), what is the 12th term of the second sequence where A_1 = 50 and r = 1/2?

• 25/1224

• 50/1224

• 50/2048

• 25/2048

Why do we convert the 12th term of the second sequence to a fraction?

• To avoid decimal approximation.

• To make it easier to read.

• To compare with other sequences.

• To simplify the calculation.

What tool is used to calculate the 12th term in the video?

• A graphing calculator.

• A basic calculator.

• Desmos calculator.

• A scientific calculator.