Geometric and Arithmetic Sequences

The video tutorial covers the concepts of geometric sequences, focusing on finding the common ratio and using recursive and explicit formulas. It also differentiates between arithmetic and geometric sequences, explaining how to identify and work with each. The tutorial concludes with a section on writing equations in slope-intercept form, detailing how to determine the slope and y-intercept from a graph.

What is the common ratio in a geometric sequence?

• The difference between consecutive terms

• The quotient of consecutive terms

• The sum of consecutive terms

• The product of consecutive terms

How do you progress in a sequence by multiplying by two?

• Divide each term by two

• Subtract two from each term

• Multiply each term by two

• Add two to each term

What is the first term in a sequence where each term is multiplied by two?

• 8

• 1

• 4

• 2

What operation is used to progress in a sequence by dividing by two?

• Multiply each term by two

• Divide each term by two

• Add two to each term

• Subtract two from each term

In a recursive equation, how is the next term defined?

• By dividing the previous term by a constant

• By adding a constant to the previous term

• By subtracting a constant from the previous term

• By multiplying the previous term by a constant

What is the common difference in an arithmetic sequence?

• The quotient of consecutive terms

• The product of consecutive terms

• The sum of consecutive terms

• The difference between consecutive terms

What is the explicit formula for an arithmetic sequence with a first term of -2 and a common difference of -2?

• f(n) = -2 + 2n

• f(n) = -2n

• f(n) = -2 - 2n

• f(n) = 2n - 2

What is the common difference in an arithmetic sequence where each term is subtracted by two?

• 1

• 0

• 2

• -2

What is the first term in a sequence where each term is divided by three?

• 27

• 9

• 3

• 1

How do you find the next term in a sequence by dividing by three?

• Multiply each term by three

• Divide each term by three

• Add three to each term

• Subtract three from each term