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Introducing Sequences

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Making Predictions

Much of the study of mathematics involves looking for patterns. Finding patterns allows us to explain relationships and make predictions.

 

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Lesson Goals

  • Express sequences numerically and graphically, using term notation.
  • Represent sequences algebraically, using a recursion formula.
  • Represent sequences algebraically, using a general term or function notation.
  • Make connections between the different algebraic representations of sequences.

Try This

A sequence of numbers is defined as follows:

  • The first term is \(5\).
  • The second term is \(-7\).
  • Each new term, after the first two, is obtained by taking the preceding term and subtracting from it the term before it. For example:
    • The third term is equal to the second term minus the first term (i.e., the third term is \(-7-5\), or \(-12\)).
    • The fourth term is equal to the third term minus the second term. 

What is the \(100\)th term in this sequence?