Pre-calculus-First Semester (2nd Periodical)
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Questions and Answers

Which of the following sequences is an arithmetic sequence?

  • an = 1 + 2 + 3 + ... + n
  • an = 1 + 2n + 3n^2
  • an = (-1)^n
  • an = 2 - n (correct)

    • Which of the following sequences is a geometric sequence?

  • an = 2 - n
  • an = 1 + 2n + 3n^2
  • an = (-1)^n (correct)
  • an = 1 + 2 + 3 + ... + n

    • What is the value of the arithmetic series S for the sequence an = 2 - n?

  • -5 (correct)
  • 1
  • 200
  • 35

    • What is the value of the geometric series S for the sequence an = (-1)^n?

    <p>1</p> Signup and view all the answers

    What is the formula for the nth term of an arithmetic sequence?

    <p>an = a1 + (n - 1)d</p> Signup and view all the answers

    Which of the following sequences is a geometric sequence?

    <p>an = (-1)^n</p> Signup and view all the answers

    Which of the following sequences is an arithmetic sequence?

    <p>an = 2 - n</p> Signup and view all the answers

    What is the value of the arithmetic series S for the sequence $a_n = 2 - n$?

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

    What is the value of the geometric series S for the sequence $a_n = (-1)^n$?

    <p>1</p> Signup and view all the answers

    What is the formula for the nth term of an arithmetic sequence?

    <p>$a_n = 2 - n$</p> Signup and view all the answers

    Which of the following sequences is an arithmetic sequence?

    <p>$a_n = 2 - n$</p> Signup and view all the answers

    Which of the following sequences is a geometric sequence?

    <p>$a_n = (-1)^n$</p> Signup and view all the answers

    What is the formula for the nth term of an arithmetic sequence?

    <p>$a_n = 2 - n$</p> Signup and view all the answers

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

    <p>$a_n = 1 + 2 + 3 + ... + n$</p> Signup and view all the answers

    What is the value of the arithmetic series S for the sequence $a_n = 2 - n$?

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

    Which symbol is used to indicate a sum in sigma notation?

    <p>∑ (sigma)</p> Signup and view all the answers

    What is the lower limit of summation in the notation k=1n(ak)?

    <p>1</p> Signup and view all the answers

    What is the upper limit of summation in the notation k=1n(ak)?

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

    What is the value of the sum i=052i?

    <p>63</p> Signup and view all the answers

    How can the sum 1 + 12 + 13 + 14 + … + 1100 be written in sigma notation?

    <p>i=11001n</p> Signup and view all the answers

    Which symbol is used to indicate a sum in sigma notation?

    <p>∑ (sigma)</p> Signup and view all the answers

    What is the lower limit of summation in the notation k=1n(ak)?

    <p>1</p> Signup and view all the answers

    What is the upper limit of summation in the notation k=1n(ak)?

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

    How can the sum 1 + 12 + 13 + 14 + … + 1100 be written in sigma notation?

    <p>$\sum_{i=1}^{100} i$</p> Signup and view all the answers

    What is the value of the sum i=052i?

    <p>63</p> Signup and view all the answers

    Which of the following is the correct expansion of the summation $i=24(2i+3)$?

    <p>$2(2) + 3 + 2(3) + 3 + 2(4) + 3 = 27$</p> Signup and view all the answers

    What is the value of the summation $k=03(-1)^k3$?

    <p>$0 - 1 + 8 - 27 = -20$</p> Signup and view all the answers

    What is the value of the summation $n=16nn+1$?

    <p>$12 + 23 + 34 + 25 + 56 + 67 = 252$</p> Signup and view all the answers

    Which of the following is the correct sigma notation for the sum 1 + 12 + 13 + 14 + … + 1100?

    <p>$i=11001n$</p> Signup and view all the answers

    Which of the following is the correct sigma notation for the sum 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9?

    <p>$k=19(-1)^{k+1}k$</p> Signup and view all the answers

    Which property of sigma notation states that the constant 'c' can be factored out of the summation?

    <p>Property 1</p> Signup and view all the answers

    In the series i=143, what is the value of the summation?

    <p>28</p> Signup and view all the answers

    In the series i=162, what is the value of the summation?

    <p>12</p> Signup and view all the answers

    Which property of sigma notation states that the constant 'c' can be factored out of the individual terms within the summation?

    <p>Property 2</p> Signup and view all the answers

    In the series i=143ai=3, what is the value of the summation?

    <p>30</p> Signup and view all the answers

    Which of the following properties of sigma notation states that a constant 'c' can be factored out of the individual terms within the summation?

    <p>Property 1</p> Signup and view all the answers

    In the series $i=1ncai=ci=1nai$, what is the value of the summation?

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

    What is the value of the series $i=1ncai$ if $a_i = 3$ and $c = 2$?

    <p>6n</p> Signup and view all the answers

    What is the value of the series $i=1ncai$ if $a_i = i$ and $c = 1$?

    <p>n(n+1)/2</p> Signup and view all the answers

    Which of the following properties of sigma notation states that the upper limit of summation can be factored out of the individual terms within the summation?

    <p>Property 2</p> Signup and view all the answers

    Which property of sigma notation states that a constant 'c' can be factored out of the individual terms within the summation?

    <p>Property 2</p> Signup and view all the answers

    In the series $i=143ai=3$, what is the value of the summation?

    <p>12</p> Signup and view all the answers

    In the series $i=162$, what is the value of the summation?

    <p>12</p> Signup and view all the answers

    In the series $i=159$, what is the value of the summation?

    <p>45</p> Signup and view all the answers

    Which of the following sequences is a geometric sequence?

    <p>1, 4, 9, 16, 25</p> Signup and view all the answers

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