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Discovering Arithmetic Sequences: Patterns & Formulas

Learn how to identify and create arithmetic sequences using common differences. Practice finding the next term and nth term of sequences with examples. Explore explicit and recursive formulas.

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Discovering Arithmetic Sequences: Patterns & Formulas

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  1. Lesson 3A:Arithmetic Sequences

  2. Ex 1: Can you find a pattern and use it to guess the next term? A) 7, 10, 13, 16,... B) 14, 8, 2, − 4, ... C) 1, 4, 9, 16,...

  3. Definition: • An arithmetic sequence is a sequence made by adding or subtracting the same value each time.

  4. Explicit Formula • a, a + d, a + 2d, a + 3d … • d = common difference • a = 1st term • nth term:

  5. Ex 2: So which examples were arithmetic sequences? Identify d and a. Write the formula for an. • A) 7, 10, 13, 16,... • B) 14, 8, 2, − 4, ... • C) 1, 4, 9, 16,...

  6. Ex 3: The formuladescribes an arithmetic sequence. What are the first 4 terms in the sequence?

  7. Ex 4: Find the first 4 terms and the nth term: a = 2 & d = 3a1= a2= a3= a4=an=

  8. Ex 5: Write an explicit formula for the following sequence: 9, 4, –1, –6, –11, … a = d = an =

  9. Recursive Formula • A recursive formula is a formula that expresses any term an in terms of the previous term an−1

  10. Ex 6: Write a recursive formula for the following sequence: • -2, -6, -10, -14, …

  11. Cool Math! • https://www.youtube.com/watch?v=wTlw7fNcO-0 • https://www.youtube.com/watch?v=SjSHVDfXHQ4 • https://www.youtube.com/watch?v=ahXIMUkSXX0

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