Test Your Math Skills
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Questions and Answers

What is the difference between an arithmetic sequence and a geometric sequence?

  • The difference between successive terms is constant in an arithmetic sequence, while the ratio between successive terms is constant in a geometric sequence.
  • Both arithmetic and geometric sequences have a constant difference between successive terms.
  • The difference between successive terms is constant in a geometric sequence, while the ratio between successive terms is constant in an arithmetic sequence. (correct)
  • Both arithmetic and geometric sequences have a constant ratio between successive terms.
  • What is the recursive definition for a geometric sequence with initial term a and common ratio r?

  • a_n = a_{n-1} - r; a_0 = a
  • a_n = a_{n-1} + r; a_0 = a
  • a_n = a_{n-1} / r; a_0 = a
  • a_n = a_{n-1} * r; a_0 = a (correct)
  • If a sequence starts with a_1 instead of a_0, how can we find the term that would have been a_0?

  • Add the common ratio to a_1.
  • Subtract the common difference from a_1.
  • Divide a_1 by the common difference.
  • Subtract the first term from a_1 and divide the result by the common difference. (correct)
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