Gr 11 Math Ch 3: Quadratic Sequences
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Questions and Answers

What is the defining characteristic of a quadratic sequence?

  • The sequence is always increasing.
  • The second difference between any two consecutive terms is constant. (correct)
  • The first difference between any two consecutive terms is constant.
  • The sequence begins with a constant term.

    • What is the general form of the nth term of a quadratic sequence?

  • Tn = an^2 + bn + c (correct)
  • Tn = an^2 - bn + c
  • Tn = an + bn^2
  • Tn = an^3 + bn^2 + c

    • How can you determine the values of a, b, and c in a quadratic sequence?

  • By solving simultaneous equations derived from the first few terms (correct)
  • By graphing the sequence and finding the vertex
  • By using the formula Tn = an^2 + bn + c
  • By finding the average of the first few terms

    • What is the first difference in a quadratic sequence?

    <p>The difference between consecutive terms</p> Signup and view all the answers

    What can be said about the second differences in a quadratic sequence?

    <p>They are always constant.</p> Signup and view all the answers

    What is the purpose of finding the first difference in a quadratic sequence?

    <p>To find the second difference of the sequence.</p> Signup and view all the answers

    If a quadratic sequence has the terms 2, 5, 10, and 17, what can be said about the sequence?

    <p>The sequence is quadratic.</p> Signup and view all the answers

    What is the advantage of knowing the general term of a quadratic sequence?

    <p>It allows us to find any term in the sequence without knowing the preceding terms.</p> Signup and view all the answers

    How many terms of a quadratic sequence are needed to determine the values of a, b, and c?

    <p>3</p> Signup and view all the answers

    What is the relationship between the general term of a quadratic sequence and the values of a, b, and c?

    <p>The general term is dependent on the values of a, b, and c.</p> Signup and view all the answers

    If a quadratic sequence has the terms 3, 6, 11, and 18, what is the value of the second term in the sequence when the first term is 5?

    <p>9</p> Signup and view all the answers

    Which of the following is a condition for a sequence to be quadratic?

    <p>The second difference is constant.</p> Signup and view all the answers

    If the nth term of a quadratic sequence is given by $T_n = an^2 + bn + c$, what can be said about the coefficients a, b, and c?

    <p>They are dependent on the values of the first few terms.</p> Signup and view all the answers

    What is the purpose of finding the general term of a quadratic sequence?

    <p>To find any term in the sequence.</p> Signup and view all the answers

    If a quadratic sequence has the terms 1, 4, 9, and 16, what can be said about the sequence?

    <p>The sequence is quadratic.</p> Signup and view all the answers

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