Sequences

• What is a sequence?


  A list of numbers usually with a rule connecting them
• What defines an arithmetic sequence?

  It has a common difference between terms
• What is another name for an arithmetic sequence?

  Linear sequence
• What characterizes a geometric sequence?


  It has a common ratio between terms
• How do you find the common difference in an arithmetic sequence?

  Subtract consecutive terms
• What does the 0th term represent in an arithmetic sequence?

  It indicates the starting point
• What is the common difference in the sequence 5, 3, 1, -1?

  -2
• What is the 10th term of the sequence with a common difference of -10 starting from -15?

  -115
• What is the common difference in the sequence -25, -35, -45, -55?

  -10
• What is the nth term formula for the sequence with a common difference of 12 starting from -35?

  $-35 +$$12n$
• What is the sequence of square numbers starting from 1?

  1, 4, 9, 16, 25
• How is a quadratic sequence defined?

  It has the highest power of 2
• What is the Fibonacci sequence?

  1, 1, 2, 3, 5, 8, 13, 21
• How do you find the next term in a Fibonacci sequence?

  Add the previous two terms together
• What are the types of sequences mentioned?

  • Arithmetic sequence
  • Geometric sequence
  • Quadratic sequence
  • Fibonacci sequence
• What are the steps to find the nth term of an arithmetic sequence?


  1. Find the common difference
  2. Identify the 0th term
  3. Combine both to form nth term
• What are the properties of quadratic and cubic sequences?

  • Quadratic: highest power of 2
  • Cubic: highest power of 3
• What is the role of common differences in sequences?

  • Determines the pattern in arithmetic sequences
• What is the role of common ratios in sequences?

  • Determines the pattern in geometric sequences
• What is the significance of the Fibonacci sequence?

  • Each term is the sum of the two previous terms