Arithmetic Sequences and Their Formulas

This video tutorial explains how to relate the explicit formula for arithmetic sequences to linear functions. It covers the explicit formula, compares it with the slope-intercept form of linear functions, and demonstrates how to write an equation using the formula. An example is provided to find the 16th term of a sequence using the explicit formula. The video concludes with a call to action for viewers to like and subscribe.

What is the explicit formula for an arithmetic sequence?

• a_n = a_1 * d(n - 1)

• a_n = a_1 - d(n - 1)

• a_n = a_1 + d(n - 1)

• a_n = a_1 + d(n + 1)

In the explicit formula a_n = a_1 + d(n - 1), what does 'd' represent?

• The common difference

• The nth term

• The slope

• The first term

How does the explicit formula for an arithmetic sequence relate to the slope-intercept form of a linear function?

• a_n replaces y, a_1 replaces the y-intercept, and d replaces x

• a_n replaces x, a_1 replaces the y-intercept, and d replaces the slope

• a_n replaces y, a_1 replaces the y-intercept, and d replaces the slope

• a_n replaces y, a_1 replaces the slope, and d replaces the y-intercept

What does the comparison between the explicit formula and the slope-intercept form tell us about the graph of an arithmetic sequence?

• It will be a parabola

• It will be a straight line

• It will be a circle

• It will be a curve

What is the first term (a_1) in the given arithmetic sequence example?

• 3

• 5

• Negative 4

• 2

How do you find the common difference (d) in an arithmetic sequence?

• By multiplying any term by the previous term

• By subtracting any term from the previous term

• By dividing any term by the previous term

• By adding any term to the previous term

What is the simplified form of the equation a_n = -4 + 3(n - 1)?

• a_n = -7 + 3n

• a_n = -4 + 3n

• a_n = -1 + 3n

• a_n = -7 + 2n

What is the value of a_16 in the given arithmetic sequence?

• 41

• 48

• 35

• 39

How do you find the 16th term in an arithmetic sequence using the explicit formula?

• By adding 16 to the first term

• By multiplying the common difference by 16

• By substituting 16 for n in the explicit formula

• By subtracting 16 from the first term

What is the main advantage of using the explicit formula in arithmetic sequences?

• It allows finding the slope

• It helps in finding the common difference

• It allows finding any term without calculating all previous terms

• It helps in finding the first term