Recursive and Explicit Formulas in Sequences

The video tutorial explains how to convert recursive formulas into explicit formulas using examples. It starts by defining the recursive formula and identifying the first term and common ratio. The tutorial then demonstrates the conversion process with three examples, highlighting the importance of identifying the initial term and the common ratio to form the explicit formula.

What is the first term in the sequence if G sub 1 is given as 3?

• 4

• 2

• 3

• 1

In the first example, what does the number 3 represent in the recursive formula?

• The first term

• The common ratio

• The exponent

• The last term

How is the explicit formula structured in the first example?

• G subn = G sub 1 + R raised to the n-1

• G subn = G sub 1 * R raised to the n-1

• G subn = G sub 1 / R raised to the n-1

• G subn = G sub 1 - R raised to the n-1

In the first example, what operation is performed repeatedly to find subsequent terms?

• Division

• Multiplication

• Subtraction

• Addition

What is the common ratio in the second example?

• 1/5

• 1/4

• 1/3

• 1/2

In the second example, what is the first term of the sequence?

• 20

• 50

• 100

• 10

How is the explicit formula structured in the second example?

• G subn = 50 * 1/5 raised to the n-1

• G subn = 50 + 1/5 raised to the n-1

• G subn = 50 / 1/5 raised to the n-1

• G subn = 50 - 1/5 raised to the n-1

In the second example, what operation is performed repeatedly to find subsequent terms?

• Division

• Multiplication

• Subtraction

• Addition

What is the first term in the third example?

• 12

• 8

• 5

• 10

In the third example, what is the common ratio?

• 13

• 11

• 10

• 12