3.4 Sequences and Series

Cards (120)

  • What is a sequence in mathematics?
    Ordered list of numbers
  • What defines an arithmetic sequence?
    Constant difference
  • What is the sum of the arithmetic sequence 2, 5, 8, 11, 14?
    40
  • A geometric sequence has a constant ratio
  • If the ratio between consecutive terms is constant, the sequence is geometric.

    True
  • In a sequence, each number is called a term
  • The common difference in an arithmetic sequence is constant.
    True
  • A geometric sequence has a constant ratio
  • Steps to identify arithmetic or geometric sequences:
    1️⃣ Check differences or ratios
    2️⃣ If difference is constant, it's arithmetic
    3️⃣ If ratio is constant, it's geometric
  • The common ratio in a geometric sequence is denoted by the variable 'r'.

    True
  • What does `d` represent in the arithmetic series sum formula?
    Common difference
  • What is the formula for the sum of the first n terms in an arithmetic series?
    S_{n} = \frac{n}{2} \left( 2a_{1} + (n - 1)d \right)</latex>
  • The sum of the geometric series 2 + 6 + 18 + 54 + 162 is 242.

    True
  • The formula for the nth term in a geometric sequence is an=a_{n} =a1⋅rn−1 a_{1} \cdot r^{n - 1}
  • What is the sum of the series 2 + 4 + 6 + 8 + 10?
    30
  • A sequence represents the cumulative sum of its terms.
    False
  • What is the common difference in an arithmetic sequence?
    Constant difference
  • Give an example of a geometric sequence.
    2, 6, 18, 54, 162
  • The common ratio in a geometric sequence can be a fraction.
    True
  • An arithmetic sequence has a constant difference between terms.

    True
  • An arithmetic sequence has a constant ratio between terms.
    False
  • An arithmetic sequence has a constant difference between terms.

    True
  • An arithmetic sequence has a constant ratio between terms.
    False
  • An arithmetic sequence is defined by a constant difference
  • A geometric sequence is a sequence with a constant ratio
  • What do you check to identify whether a sequence is arithmetic or geometric?
    Differences or ratios
  • Match the sequence type with its identifying factor:
    Arithmetic ↔️ Constant difference
    Geometric ↔️ Constant ratio
  • In an arithmetic sequence, 'd' represents the common difference between terms.

    True
  • In a geometric sequence, the ratio between consecutive terms is called the common ratio
  • Checking differences or ratios helps determine if a sequence is arithmetic or geometric.

    True
  • A series is the sum of the terms in a sequence.
    True
  • The common difference in an arithmetic sequence is constant.

    True
  • Match the sequence type with its defining characteristic:
    Arithmetic sequence ↔️ Constant difference
    Geometric sequence ↔️ Constant ratio
  • Steps to identify whether a sequence is arithmetic or geometric
    1️⃣ Check differences between consecutive terms
    2️⃣ If difference is constant, it's arithmetic
    3️⃣ If ratio is constant, it's geometric
  • Match the sequence type with its identifying factor:
    Arithmetic ↔️ Constant difference
    Geometric ↔️ Constant ratio
  • The series 2 + 4 + 6 + 8 + 10 has a sum of 30.

    True
  • The common difference in the sequence 2, 5, 8, 11, 14 is 3
  • The common ratio in a geometric sequence is constant.

    True
  • An arithmetic sequence has a constant ratio between terms.
    False
  • What is the formula for the sum of the first n terms in an arithmetic series?
    Sn=S_{n} = \frac{n}{2} \left( 2a_{1} + (n - 1)d \right)