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Geometric Sequences quiz

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  • What is the defining characteristic of a geometric sequence?
    A geometric sequence is defined by a constant multiplier, called the common ratio, between consecutive terms.
  • How do you identify the common ratio in a geometric sequence?
    You identify the common ratio by dividing any term by its previous term.
  • What is the general formula for the nth term of a geometric sequence?
    The general formula is an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.
  • How do you find the next term in a geometric sequence?
    Multiply the current term by the common ratio to get the next term.
  • If the first term is 5 and the second term is 20, what is the common ratio?
    The common ratio is 4, since 20 divided by 5 equals 4.
  • What makes a sequence arithmetic instead of geometric?
    An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio.
  • How can dividing by a number in a sequence be interpreted in terms of the common ratio?
    Dividing by a number is the same as multiplying by its reciprocal, which becomes the common ratio.
  • What is the common ratio in the sequence 9, 3, 1, 1/3?
    The common ratio is 1/3, since each term is multiplied by 1/3 to get the next.
  • How do you write the second term of a geometric sequence using the first term and the common ratio?
    The second term is the first term multiplied by the common ratio: a2 = a1 * r.
  • In the sequence 3, 6, 12, 24, what is the formula for the nth term?
    The nth term is an = 3 * 2^(n-1).
  • How do you find the value of the 20th term in a geometric sequence with a1 = 3 and r = 2?
    Calculate 3 * 2^19 to find the 20th term.
  • What is the common ratio in the sequence 16/27, 8/9, 3/4, 2?
    The common ratio is 3/2, found by dividing 8/9 by 16/27.
  • How do you express the nth term for the sequence with a1 = 8 and r = 3?
    The nth term is an = 8 * 3^(n-1).
  • What operation do you perform to find the common ratio when terms are fractions?
    Divide one term by the previous term, which may involve multiplying by the reciprocal.
  • Why is the exponent in the general term formula (n-1) instead of n?
    Because the first term is multiplied by the common ratio zero times, so the exponent is always one less than the term's position.