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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 notation used for the nth term of a sequence?
    The nth term is denoted as a sub n, written as a_n.
  • How do you determine if a sequence is finite or infinite?
    A sequence is finite if the index n is restricted to a certain maximum value; otherwise, it is infinite.
  • What is the first term of the sequence with general term a_n = 2^n?
    The first term is 2, found by plugging n = 1 into the formula.
  • How do you write the explicit formula for a sequence that increases by a constant amount each time?
    The explicit formula will include n multiplied by the constant difference, possibly adjusted by adding or subtracting a constant.
  • What pattern in a sequence suggests using (-1)^n in the formula?
    A sequence that alternates signs, such as negative, positive, negative, positive, suggests using (-1)^n.
  • How do you adjust a formula if the first term does not match the index value?
    You add or subtract a constant to the formula so that plugging in n = 1 gives the correct first term.
  • What is the general formula for the sequence 1/2, 2/3, 3/4, 4/5, 5/6?
    The general formula is a_n = n/(n+1).
  • How do you recognize an exponential sequence?
    An exponential sequence has terms that are powers of a base, such as 2, 4, 8, 16, which are all powers of 2.
  • What is the explicit formula for the sequence 5, 6, 7, 8, 9?
    The explicit formula is a_n = n + 4.
  • How do you find all terms of a finite sequence defined by a_n = 4 - n for 1 ≤ n ≤ 6?
    Plug in n = 1 through n = 6 into the formula to get all terms: 3, 2, 1, 0, -1, -2.
  • What does the notation a_10 represent in a sequence?
    a_10 represents the 10th term of the sequence, found by plugging n = 10 into the general term.
  • Why might you need to multiply by a constant in a sequence formula with alternating signs?
    Multiplying by a constant adjusts the magnitude of the terms to match the sequence values.
  • What is an explicit formula in the context of sequences?
    An explicit formula is an equation involving n that allows you to find any term in the sequence directly.