Toothpick Patterns and Sequences

The video tutorial introduces sequences and series in Algebra 2, highlighting their parallels to linear and exponential functions. It defines sequences, terms, and the notation used. The tutorial explains explicit and recursive formulas, providing examples of each. Explicit formulas allow direct calculation of any term, while recursive formulas build terms from previous ones. The video concludes with examples of both formula types, emphasizing their applications in finding sequence terms.

What is the main focus of the next unit in Algebra 2?

• Linear functions

• Sequences and series

• Exponential functions

• Quadratic functions

Which of the following is NOT a type of sequence discussed?

• Geometric

• Fibonacci

• Harmonic

• Arithmetic

What does a subscript in sequence notation indicate?

• The value of the term

• The position of the term

• The type of sequence

• The sum of the sequence

How is an explicit formula used in sequences?

• To find the common difference

• To find the first term

• To find the nth term directly

• To find the sum of all terms

What is the benefit of using an explicit formula over a recursive formula?

• It is more accurate

• It is easier to understand

• It allows direct calculation of any term

• It requires fewer calculations

What is a key characteristic of a recursive formula?

• It is used only for geometric sequences

• It is used only for arithmetic sequences

• It directly finds the nth term

• It requires previous terms to find the next term

Using the explicit formula a_n = 7n + 2, what is the first term?

• 14

• 9

• 2

• 7

What is the 5th term in the sequence defined by a_n = 7n + 2?

• 30

• 51

• 37

• 44

What is the common difference in the sequence defined by a_n = 7n + 2?

• 5

• 6

• 7

• 8

What is the 10th term in the sequence defined by a_n = 7n + 2?

• 79

• 72

• 86

• 65