Math Gr 8 Ch 5: Investigate and Extend Patterns
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Questions and Answers

What is the formula for the nth term of a sequence with a constant difference?

  • T_n = n^2
  • T_n = T_1 + (n - 1) \cdot d (correct)
  • T_n = a \cdot n + b
  • T_n = T_1 \cdot r^{(n-1)}

    • What is the formula for the nth term of a geometric sequence?

  • T_n = T_1 + (n - 1) \cdot d
  • T_n = n^2
  • T_n = T_1 \cdot r^{(n-1)} (correct)
  • T_n = a \cdot n + b

    • What is the formula for the nth term of a sequence that follows a linear pattern?

  • T_n = n^2
  • T_n = T_1 + (n - 1) \cdot d
  • T_n = T_1 \cdot r^{(n-1)}
  • T_n = a \cdot n + b (correct)

    • What is the formula for the nth triangular number?

    <p>T_n = rac{n \cdot (n + 1)}{2}</p> Signup and view all the answers

    What is the formula for the nth square number?

    <p>T_n = n^2</p> Signup and view all the answers

    Which type of sequence has a constant ratio?

    <p>Geometric sequence</p> Signup and view all the answers

    Which sequence would have a constant difference between consecutive terms?

    <p>A sequence with a linear pattern</p> Signup and view all the answers

    If a sequence has a constant ratio, what is the relationship between the nth term and the first term?

    <p>The nth term is the first term multiplied by the ratio to the power of n minus 1.</p> Signup and view all the answers

    What is the general form of a sequence that follows a linear pattern?

    <p>Tn = an + b</p> Signup and view all the answers

    What is the relationship between the number of elements in the nth position of a triangular number pattern?

    <p>The number of elements is equal to n times n plus 1 divided by 2.</p> Signup and view all the answers

    How can you describe the pattern of a sequence with a geometric progression?

    <p>It follows a geometric pattern with a constant ratio.</p> Signup and view all the answers

    What is the formula for the nth term of a sequence with a T-shaped pattern?

    <p>Tn = T1 + (n - 1) * d</p> Signup and view all the answers

    If a sequence has a constant difference of 3, and the 5th term is 17, what is the 10th term?

    <p>35</p> Signup and view all the answers

    A sequence follows a geometric progression with a ratio of 2. If the 3rd term is 16, what is the 6th term?

    <p>256</p> Signup and view all the answers

    The number of elements in a triangular number pattern is given by the formula $T_n = \frac{n \cdot (n + 1)}{2}$. If the 5th term has 15 elements, what is the term number of a triangular number pattern with 21 elements?

    <p>7</p> Signup and view all the answers

    A sequence follows a linear pattern with a common difference of 2. If the 2nd term is 5, what is the equation that represents the sequence?

    <p>$T_n = 2n + 3$</p> Signup and view all the answers

    The number of elements in a square number pattern is given by the formula $T_n = n^2$. If the 4th term has 16 elements, what is the term number of a square number pattern with 25 elements?

    <p>5</p> Signup and view all the answers

    A sequence has a constant ratio of 3. If the 2nd term is 9, what is the 5th term?

    <p>81</p> Signup and view all the answers

    What is the correct formula for the nth term of a sequence with a constant difference, if the first term is 5 and the common difference is 2?

    <p>T_n = 5 + (n - 1) \cdot 2</p> Signup and view all the answers

    A sequence follows a geometric progression with a ratio of 4. If the 2nd term is 12, what is the 5th term?

    <p>12 \cdot 4^3</p> Signup and view all the answers

    What is the correct equation for the nth term of a sequence that follows a linear pattern, if the 1st term is 3 and the common difference is 5?

    <p>T_n = 3 + (n - 1) \cdot 5</p> Signup and view all the answers

    A triangular number pattern has a formula of $T_n = rac{n \cdot (n + 1)}{2}$. If the 4th term has 10 elements, what is the term number of a triangular number pattern with 28 elements?

    <p>7</p> Signup and view all the answers

    What is the correct formula for the nth term of a sequence with a geometric progression, if the first term is 2 and the common ratio is 3?

    <p>T_n = 2 \cdot 3^(n - 1)</p> Signup and view all the answers

    A sequence follows a linear pattern with a common difference of -2. If the 3rd term is -5, what is the equation that represents the sequence?

    <p>T_n = -5 + (n - 3) \cdot (-2)</p> Signup and view all the answers

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