Introduction to Sequences

Intro to Arithmetic Sequences

Definitions

• What does n mean?

  n is the order that a term in a sequence occurs

  Example: In the sequence 1, 3, 5, 7,... “5” is the 3rd term, so the value of n would be 3

• What does t(n) mean?

  t(n) is the “nth” term

  Example: If I want to find the 7th term in the sequence, I’m looking for t(7)

• What is a common difference? It is the number being added every time in an arithmetic sequence

Multiple Choice

In the sequence 2, 4, 6, 7, ... What is the value of n for 7?

• 3

• 4

• 7

• 1

Multiple Choice

If I want to find t(4), what am I looking for?

• The 4th term

• How many times 4 occurs in the sequence

• The position of 4 in the sequence

• What the sequence would look like if it was multiplied by 4

Multiple Choice

In the sequence -7, 1, 9, 17, 25, ... What is the common difference?

• 10

• 4

• -8

• 8

Explicit Equations for Arithmetic Sequences

• Remember that arithmetic sequences are basically just linear equations. You’re just replacing x and y with n and t(n)

  Common difference = slope

  t(0) or “0th term” = y-intercept

  
  

• Example: if your common difference was -3, and t(0) = 7, your equation would be t(n) = -3n + 7

Multiple Choice

If the common difference is 4 and t(0) = 5, what would the equation for the sequence be?

• y = 4x + 5

• t(n) = 5n + 4

• t(n) = 4n + 5

• y = 5x + 4