Exponential Sequences and Recursive Formulas

The video tutorial explains how to express exponential patterns using recursive formulas. It covers the basics of recursive formulas, compares them with explicit formulas, and provides steps to write recursive formulas for exponential sequences. The tutorial also generalizes the process for exponential relationships, emphasizing the importance of identifying the starting term and constant multiplier.

What is the primary purpose of a recursive formula?

• To determine the last term in a sequence

• To calculate the sum of all terms

• To find the next term based on the previous term

• To list all terms in a sequence

In the example sequence, what is the value of the first term (t sub 1)?

• 2

• 8

• 3

• 5

How do you find the value of t sub 3 in the given recursive sequence?

• Add 3 to t sub 2

• Multiply t sub 2 by 2

• Subtract 1 from t sub 2

• Add 5 to t sub 2

What is a key difference between recursive and explicit formulas?

• Recursive formulas require all previous terms to find the next term

• Explicit formulas are always more accurate

• Explicit formulas require all previous terms to find the next term

• Recursive formulas are always more accurate

What is the explicit formula for the sequence discussed in the video?

• t sub n = 2n - 1

• t sub n = 2n + 1

• t sub n = 3n - 1

• t sub n = 3n + 1

What is the constant multiplier in the exponential sequence example?

• 0.5

• 3

• 2

• 1

How do you determine the next term in an exponential sequence using a recursive formula?

• Add a constant to the previous term

• Multiply the previous term by a constant multiplier

• Subtract a constant from the previous term

• Divide the previous term by a constant

What is the first step in determining a recursive formula for an exponential relationship?

• Establish where the pattern begins

• Find the constant multiplier

• Identify the last term

• Calculate the sum of all terms

What is the second step in determining a recursive formula for an exponential relationship?

• Establish where the pattern begins

• Calculate the sum of all terms

• Find the constant multiplier

• Identify the last term

What is the final step in writing a recursive formula for an exponential relationship?

• State the beginning term and then t sub n equals b times t sub n minus 1

• Find the constant multiplier

• Identify the last term

• Calculate the sum of all terms