Geometric Sequences Quiz

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Questions and Answers

Which term best describes a sequence where each term is obtained by multiplying the previous term by a constant number?

  • Prime sequence
  • Arithmetic sequence
  • Fibonacci sequence
  • Geometric sequence (correct)

What is the common ratio of a geometric sequence if the first term is 2 and the second term is 6?

  • 4
  • 1
  • 3 (correct)
  • 2

If the first term of a geometric sequence is 3 and the common ratio is 0.5, what is the third term?

  • 1.5 (correct)
  • 1
  • 0
  • 2

Which term best describes a sequence where each term is obtained by adding a constant number to the previous term?

<p>Arithmetic sequence (B)</p> Signup and view all the answers

What is the formula to find the nth term of an arithmetic sequence?

<p>$a_n = a_1 + (n-1)d$ (C)</p> Signup and view all the answers

If the first term of an arithmetic sequence is 3 and the common difference is 4, what is the 6th term?

<p>23 (D)</p> Signup and view all the answers

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Study Notes

Geometric Sequence

  • A geometric sequence is a sequence where each term is obtained by multiplying the previous term by a constant number.
  • The common ratio of a geometric sequence can be found by dividing the second term by the first term.
  • For example, if the first term is 2 and the second term is 6, the common ratio is 6/2 = 3.
  • If the first term of a geometric sequence is 3 and the common ratio is 0.5, the third term is 3 × 0.5 × 0.5 = 0.75.

Arithmetic Sequence

  • An arithmetic sequence is a sequence where each term is obtained by adding a constant number to the previous term.
  • The formula to find the nth term of an arithmetic sequence is an = a1 + (n-1)d, where a1 is the first term and d is the common difference.
  • For example, if the first term of an arithmetic sequence is 3 and the common difference is 4, the 6th term is 3 + (6-1)4 = 3 + 20 = 23.

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