Arithmetic Sequences and Formulas

This video tutorial introduces arithmetic sequences, explaining both recursive and explicit formulas. Using a warehouse example, it demonstrates how to solve sequence problems and relates sequences to linear functions. The tutorial covers different types of sequence problems and provides methods to derive definitions from sequences, concluding with a recap and final example.

What is an arithmetic sequence?

• A sequence where each term is obtained by adding a constant to the previous term.

• A sequence where each term is the square of the previous term.

• A sequence where each term is the sum of the previous two terms.

• A sequence where each term is a constant multiple of the previous term.

In the warehouse scenario, how many boxes are there initially?

• 50 boxes

• 37 boxes

• 40 boxes

• 43 boxes

What is the common difference in the warehouse scenario?

• 4

• 3

• 2

• 5

How is a recursive formula defined?

• By specifying the first term and a rule to find the next term from the previous one.

• By specifying the last term and a rule to find the previous term from the next one.

• By specifying a formula that directly calculates any term.

• By specifying a formula that calculates the sum of all terms.

What is the explicit formula for the number of boxes on day n?

• a_n = 37 + 3n

• a_n = 40 + 3n

• a_n = 37 + 2n

• a_n = 40 + 2n

How does the slope-intercept form relate to arithmetic sequences?

• The slope is the product of terms, and the y-intercept is the last term.

• The slope is the initial term, and the y-intercept is the common difference.

• The slope is the sum of terms, and the y-intercept is the average term.

• The slope is the common difference, and the y-intercept is the initial term.

What is the first step in solving sequence problems using a recursive definition?

• Find the last term.

• Determine the initial term.

• Calculate the sum of all terms.

• Identify the common difference.

How can you find the common difference from two terms in a sequence?

• By dividing the larger term by the smaller term.

• By multiplying the two terms.

• By subtracting the smaller term from the larger term.

• By adding the two terms.

What is the recursive formula for a sequence starting at 54 with a common difference of -3?

• a_n = a_(n-1) - 2

• a_n = a_(n-1) - 3

• a_n = a_(n-1) + 3

• a_n = a_(n-1) + 2

If a sequence has a common difference of 6, what is the explicit formula starting from 10?

• a_n = 6 - 10n

• a_n = 6 + 10n

• a_n = 10 - 6n

• a_n = 10 + 6n