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Arithmetic Sequences quiz

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이 집합의 용어 (15)

  • What is an arithmetic sequence?
    An arithmetic sequence is a sequence where each term differs from the previous one by a constant amount called the common difference.
  • How do you recognize an arithmetic sequence?
    You recognize an arithmetic sequence if the difference between consecutive terms is always the same.
  • What is the common difference in an arithmetic sequence?
    The common difference, denoted as d, is the fixed amount added or subtracted to each term to get the next term.
  • How do you calculate the common difference d?
    You subtract any term from the next consecutive term, such as d = a2 - a1.
  • If the first term is 2 and the second term is 6, what is the common difference?
    The common difference is 6 - 2 = 4.
  • What does a negative common difference indicate in an arithmetic sequence?
    A negative common difference means you subtract the same value each time to get the next term.
  • What is the formula for the nth term (general term) of an arithmetic sequence?
    The formula is an = a1 + (n - 1) × d, where a1 is the first term and d is the common difference.
  • How do you use the general term formula to find the 20th term of a sequence?
    Plug n = 20 into the formula: a20 = a1 + (20 - 1) × d.
  • If a sequence starts at 10 and decreases by 2 each time, what are the next two terms after 8?
    The next two terms are 6 and 4.
  • How do you find the common difference if you know the first and fifth terms?
    Set up the equation a5 = a1 + 4d, plug in the values, and solve for d.
  • What information do you need to write the general term of an arithmetic sequence?
    You need the first term (a1) and the common difference (d).
  • How can you simplify the general term formula an = 2 + (n - 1) × 4?
    Distribute and combine like terms to get an = 4n - 2.
  • If a1 = 8 and d = -6, what is the general term formula?
    The general term is an = 8 + (n - 1) × (-6).
  • If a1 = 2 and a5 = 14, what is the common difference?
    The common difference is 3, found by solving 14 = 2 + 4d.
  • Why is the formula an = a1 + (n - 1)d useful?
    It allows you to find any term in the sequence quickly without listing all previous terms.