Exploring Arithmetic and Geometric Sequences

The video tutorial by Kirk Wier covers arithmetic and geometric sequences in Common Core Algebra 2. It begins with an introduction to sequences, followed by a detailed explanation of arithmetic sequences, including their recursive definition and examples. The tutorial then shifts focus to geometric sequences, explaining their definition and providing examples. The video concludes with a summary of the key concepts discussed.

What is required to define an arithmetic sequence?

• The sum of all terms

• The first term and the common difference

• The last term and the common ratio

• The product of all terms

How do you calculate the next term in an arithmetic sequence?

• By subtracting the common difference from the previous term

• By adding the common difference to the previous term

• By dividing the previous term by the common difference

• By multiplying the previous term by the common difference

What is the common difference in the sequence 3, 8, 13, 18?

• 3

• 2

• 15

• 5

How do you find the value of 'T' in a complex arithmetic sequence problem?

• By adding the terms together

• By setting up and solving an equation based on the common difference

• By guessing and checking different values

• By calculating the average of the terms

What defines a geometric sequence?

• The product of consecutive terms

• The ratio of consecutive terms

• The difference between consecutive terms

• The sum of consecutive terms

What is the common ratio in a geometric sequence where each term is triple the previous term?

• 2

• 1/3

• 0

• 3

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

• By multiplying the previous term by the common ratio

• By adding the common ratio to the previous term

• By subtracting the common ratio from the previous term

• By dividing the previous term by the common ratio

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

• First term plus (n-1) times the common difference

• First term times the common ratio to the power of (n-1)

• First term divided by the common ratio to the power of n

• First term minus (n-1) times the common ratio

In a geometric sequence, if the first term is 2 and the common ratio is 3, what is the fourth term?

• 54

• 24

• 18

• 81

How many times was the common ratio multiplied to get from the first to the fourth term in a geometric sequence?

• Three times

• Four times

• Once

• Twice