Geometric Sequences and Functions

This video tutorial explains the concept of geometric sequences and their representation as exponential functions. It covers function notation, evaluates functions with examples, and clarifies common misunderstandings between arithmetic and geometric sequences. The tutorial derives the explicit rule for geometric sequences and demonstrates how to graph them, highlighting their exponential growth. The video concludes by confirming that the explicit rule for a geometric sequence can be expressed as an exponential function.

What does the function notation y = f(x) represent in terms of domain and range?

• y is the domain and f(x) is the range

• x is the range and f(x) is the domain

• x is the domain and f(x) is the range

• y is the range and x is the domain

When evaluating the function f(x) = 2 * 3^(x-1), what is the value of f(3)?

• 6

• 18

• 9

• 27

Which of the following sequences is geometric?

• Subtracting 1 from each term

• Multiplying each term by 3

• Multiplying by 2, then 3, then 4

• Adding 3 to each term

What is the explicit rule for a geometric sequence with a first term of 3 and a common ratio of 3?

• a_n = 3^(n-1) * 3

• a_n = 3^(n-1) + 3

• a_n = 3 * 3^(n-1)

• a_n = 3 + 3^(n-1)

How do you verify the fifth term in a geometric sequence using the explicit rule?

• By adding the common ratio to the fourth term

• By multiplying the fourth term by the common ratio

• By dividing the fourth term by the common ratio

• By subtracting the common ratio from the fourth term

What mistake is commonly made when evaluating the explicit rule for a geometric sequence?

• Adding before multiplying

• Multiplying before simplifying exponents

• Dividing before adding

• Subtracting before dividing

In the sequence a_n = 3 * 3^(n-1), what is the value of a_3?

• 27

• 9

• 81

• 243

On a coordinate plane, what does the x-axis represent when graphing a geometric sequence?

• The term number

• The sequence sum

• The common ratio

• The term value

How is the explicit rule for a geometric sequence related to an exponential function?

• It is a quadratic function

• It is a linear function

• It is an exponential function

• It is a logarithmic function

What ordered pair represents the fifth term in the sequence a_n = 3 * 3^(n-1)?

• (5, 81)

• (5, 9)

• (5, 243)

• (5, 27)