Gr12 Mathematics: Ch 1.6 Infinite Series
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Questions and Answers

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

  • Tn = a × (n - 1) d
  • Tn = a / (n - 1) d
  • Tn = a - (n - 1) d
  • Tn = a + (n - 1) d (correct)

    • What is the sum of the first 100 positive integers?

  • 4000
  • 6000
  • 7000
  • 5050 (correct)

    • What is the general formula for a finite arithmetic series?

  • Sn = n / 2 × (a + l)
  • Sn = n × (a + l)
  • Sn = n / 2 × (2a + (n - 1) d) (correct)
  • Sn = n × (a - l)

    • What is the last term (l) in an arithmetic sequence?

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

    What is the advantage of using Karl Friedrich Gauss's method?

    <p>It is a simple and efficient method for summing a finite arithmetic series</p> Signup and view all the answers

    What is the common difference (d) in an arithmetic sequence?

    <p>The constant difference between any term and the previous term</p> Signup and view all the answers

    What is the formula for Sn when the last term l is unknown?

    <p>Sn = n / 2 × (2a + (n - 1) d)</p> Signup and view all the answers

    What is the purpose of deriving the general formula for a finite arithmetic series?

    <p>To find the sum of any finite arithmetic series</p> Signup and view all the answers

    What is the formula for the sum of an arithmetic sequence from the first term (a) to the last term (l)?

    <p>$S_n = rac{n}{2} (a + l)$</p> Signup and view all the answers

    How many terms are being added together in the sum: $S_{100} = 1 + 2 + 3 + … + 100$?

    <p>100</p> Signup and view all the answers

    What is the value of $d$ in the sequence of positive integers?

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

    What is the purpose of adding corresponding pairs of terms in Karl Friedrich Gauss's method?

    <p>To simplify the sum</p> Signup and view all the answers

    What is the value of $S_{100}$ when using Karl Friedrich Gauss's method?

    <p>5050</p> Signup and view all the answers

    What is the formula for the $n$-th term of an arithmetic sequence?

    <p>$T_n = a + (n - 1) d$</p> Signup and view all the answers

    What is the formula for $S_n$ when the last term $l$ is unknown?

    <p>$S_n = rac{n}{2} (2a + (n - 1) d)$</p> Signup and view all the answers

    What is the advantage of using formulas to calculate the sum of an arithmetic sequence?

    <p>It is faster than listing out all the terms</p> Signup and view all the answers

    What is the sum of the first 50 positive integers?

    <p>1275</p> Signup and view all the answers

    If the sum of the first 20 terms of an arithmetic sequence is 210, what is the common difference?

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

    What is the sum of the first 15 terms of an arithmetic sequence with a first term of 3 and a common difference of 2?

    <p>135</p> Signup and view all the answers

    If the sum of the first 25 terms of an arithmetic sequence is 625, what is the first term?

    <p>10</p> Signup and view all the answers

    What is the sum of the first 30 terms of an arithmetic sequence with a last term of 60 and a common difference of 2?

    <p>930</p> Signup and view all the answers

    If the sum of the first 18 terms of an arithmetic sequence is 342, what is the last term?

    <p>38</p> Signup and view all the answers

    What is the sum of the first 12 terms of an arithmetic sequence with a first term of 2 and a last term of 26?

    <p>156</p> Signup and view all the answers

    If the sum of the first 40 terms of an arithmetic sequence is 1040, what is the common difference?

    <p>4</p> Signup and view all the answers

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