Arithmetic and Geometric Sequences

The video tutorial covers geometric sequences as exponential functions. It begins with a review of previous material, introduces key vocabulary such as 'geometric sequence' and 'common ratio', and explains how to identify whether a sequence is arithmetic, geometric, or neither. The tutorial includes examples to illustrate these concepts and demonstrates how to find the next terms in a sequence. It concludes with a formula for calculating terms in a geometric sequence.

What should you do before starting the geometric sequences section?

• Read a textbook chapter.

• Skip to the end of the video.

• Complete the first five review problems.

• Watch the entire video without pausing.

What is a geometric sequence?

• A sequence where each term is subtracted by a constant.

• A sequence where each term is divided by a constant.

• A sequence where each term is added by a constant.

• A sequence where each term is multiplied by a constant.

What is the common ratio in a geometric sequence?

• The sum of all terms.

• The difference between the first and last term.

• The product of all terms.

• The ratio of successive terms.

How do you determine if a sequence is arithmetic?

• Check if there is a common ratio.

• Check if there is a common difference.

• Check if all terms are odd.

• Check if all terms are even.

In the example given, what is the common difference of the arithmetic sequence?

• 8

• 6

• 10

• 4

What is the common ratio in the geometric sequence example?

• 4/5

• 2/3

• 3/4

• 1/2

How do you find the next term in a geometric sequence?

• Divide the last term by the common ratio.

• Multiply the last term by the common ratio.

• Subtract the common difference from the last term.

• Add the common difference to the last term.

What is the formula used to find any term in a geometric sequence?

• a_n = a_1 + (n-1)d

• a_n = a_1 - (n-1)d

• a_n = a_1 / r^(n-1)

• a_n = a_1 * r^(n-1)

In the formula a_n = a_1 * r^(n-1), what does 'a_1' represent?

• The common ratio.

• The number of terms.

• The last term of the sequence.

• The first term of the sequence.

How do you find the 12th term of a geometric sequence using the formula?

• Substitute 11 for n in the formula.

• Substitute 10 for n in the formula.

• Substitute 12 for n in the formula.

• Substitute 13 for n in the formula.