Unlocking Arithmetic Sequences: Mastering the Explicit Formula

Algebra 2 Grades High School 7:38 Video
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Lesson Description

Learn how to use the explicit formula to find any term in an arithmetic sequence. This lesson covers identifying arithmetic sequences, applying the explicit formula, and solving for specific terms or positions within a sequence.

Video Resource

Arithmetic Sequence Explicit Formula

Kevinmathscience

Duration: 7:38
Watch on YouTube

Key Concepts

  • Arithmetic Sequence
  • Explicit Formula
  • Common Difference

Learning Objectives

  • Identify arithmetic sequences and determine the common difference.
  • Apply the explicit formula to find a specific term in an arithmetic sequence.
  • Determine the position of a term given its value in an arithmetic sequence.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a sequence and introducing the concept of an arithmetic sequence. Briefly discuss the difference between explicit and recursive formulas (as mentioned in the video).
  • Video Viewing (10 mins)
    Play the Kevinmathscience video "Arithmetic Sequence Explicit Formula." Instruct students to take notes on the key components of the explicit formula: A1 (first term), D (common difference), N (position number), and aN (value of the term).
  • Formula Breakdown and Examples (15 mins)
    Review the explicit formula: aN = A1 + D(N-1). Work through the examples provided in the video, pausing to ensure student understanding. Emphasize the importance of correctly identifying A1, D, and N in each problem. Work through additional example problems, varying the level of difficulty.
  • Practice Problems (15 mins)
    Provide students with a set of practice problems that require them to use the explicit formula to find specific terms and determine the position of terms within different arithmetic sequences. Circulate to provide assistance and answer questions.
  • Wrap-up and Assessment (5 mins)
    Summarize the key concepts covered in the lesson. Administer a short quiz to assess student understanding of the explicit formula and its application.

Interactive Exercises

  • Sequence Scavenger Hunt
    Provide students with a list of sequences, some arithmetic and some not. Have them identify the arithmetic sequences and determine the common difference for each.
  • Term Prediction Challenge
    Present students with an arithmetic sequence and challenge them to predict the value of a specific term (e.g., the 50th term) using the explicit formula.

Discussion Questions

  • What is the difference between an arithmetic and a geometric sequence?
  • How can you determine if a sequence is arithmetic?
  • Why is the explicit formula useful for finding terms far down the sequence?

Skills Developed

  • Problem-solving
  • Analytical thinking
  • Formula application

Multiple Choice Questions

Question 1:

Which of the following sequences is arithmetic?

Correct Answer: 3, 7, 11, 15...

Question 2:

In the arithmetic sequence 5, 10, 15, 20..., what is the common difference?

Correct Answer: 5

Question 3:

The explicit formula for an arithmetic sequence is aN = A1 + D(N-1). What does 'A1' represent?

Correct Answer: The first term

Question 4:

Given the arithmetic sequence with A1 = 2 and D = 3, what is the value of the 5th term (a5)?

Correct Answer: 14

Question 5:

In the arithmetic sequence 10, 7, 4, 1..., what is the common difference?

Correct Answer: -3

Question 6:

If a sequence is defined by aN = 4 + 2(N-1), what is the value of the third term?

Correct Answer: 8

Question 7:

If A1=3 and D=-2, what is the explicit formula for this arithmetic sequence?

Correct Answer: aN = 3 - 2(N-1)

Question 8:

What is the purpose of the explicit formula?

Correct Answer: To find any term directly without knowing the previous terms

Question 9:

An arithmetic sequence has a first term of 2 and a common difference of 4. Which term is equal to 30?

Correct Answer: 8th term

Question 10:

An arithmetic sequence has a common difference of -5, and the fifth term is -10. What is the first term?

Correct Answer: 10

Fill in the Blank Questions

Question 1:

An arithmetic sequence is a sequence where the difference between consecutive terms is ________.

Correct Answer: constant

Question 2:

The explicit formula for an arithmetic sequence is aN = A1 + D(N-1), where 'D' represents the ________.

Correct Answer: common difference

Question 3:

In an arithmetic sequence, if A1 = 4 and D = 2, the second term (a2) is ________.

Correct Answer: 6

Question 4:

The position of a term in a sequence is represented by the variable ________ in the explicit formula.

Correct Answer: N

Question 5:

If an arithmetic sequence has A1 = 10 and D = -3, then the third term is ________.

Correct Answer: 4

Question 6:

If the first term is 5 and the 10th term is 50, then the common difference is ________.

Correct Answer: 5

Question 7:

In the explicit formula, aN represents the ________ of the nth term.

Correct Answer: value

Question 8:

Given the formula aN = 7 + 3(N-1), the first term of the sequence is ________.

Correct Answer: 7

Question 9:

If a sequence starts 2, 6, 10, 14, then the common difference is ________.

Correct Answer: 4

Question 10:

The explicit formula allows you to find any term of an arithmetic sequence _______ knowing the previous terms.

Correct Answer: without

Educational Standards

A2.A.3:Represent and solve mathematical and real-world problems involving arithmetic and geometric sequences and series. A2.A.3.1:Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Using the pattern, find the next term. A2.A.3.3:Solve problems that can be modeled using arithmetic sequences or series given the ๐‘›th terms and sum formulas. Graphing calculators or other appropriate technology may be used.

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