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Introduction to Sequences quiz

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  • What is the domain of a sequence?
    The domain of a sequence is all positive integers, starting from 1 and increasing by 1 each time.
  • How do you find the nth term of a sequence given its general term?
    You substitute the index n into the general term formula to calculate the nth term.
  • What is the difference between a finite and an infinite sequence?
    A finite sequence has a limited number of terms, while an infinite sequence continues forever.
  • How do you represent the first term of a sequence using notation?
    The first term is represented as a₁, where n equals 1.
  • If a sequence is defined by aₙ = 2ⁿ, what is the third term?
    The third term is 8, since 2 to the power of 3 equals 8.
  • How do you find all terms of a finite sequence defined for n = 1 to n = 6?
    You substitute n = 1, 2, 3, 4, 5, and 6 into the general term and list each result.
  • What does it mean if a sequence increases by the same amount each time?
    It means the sequence is an arithmetic progression, and its formula includes a term like n, 2n, or 3n.
  • How do you adjust a sequence formula if the first term is not 1?
    You add or subtract a constant to shift the sequence so the first term matches the desired value.
  • What pattern in a sequence suggests using (-1)ⁿ in the formula?
    Alternating signs in the sequence indicate you should use (-1) raised to the n power.
  • How do you write a formula for a sequence with alternating signs and a constant value?
    Multiply (-1)ⁿ by the constant value to alternate the sign for each term.
  • What does it mean if a sequence contains fractions with numerators and denominators increasing by 1?
    It means the formula will have n in the numerator and n plus a constant in the denominator.
  • How do you determine the numerator and denominator in a sequence like 1/2, 2/3, 3/4?
    The numerator is n, and the denominator is n + 1.
  • What type of sequence is represented by 2, 4, 8, 16, 32?
    This is a geometric or exponential sequence, where each term is a constant raised to the n power.
  • How do you recognize an exponential pattern in a sequence?
    If the difference between terms is not constant but the ratio is, the sequence is exponential.
  • What is an explicit formula for a sequence?
    An explicit formula is an equation involving n that allows you to find any term in the sequence directly.