Grade 12 Mathematics: Sequences and Series
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Questions and Answers

What is the general formula for finding the nth term in an arithmetic sequence?

  • $T_n = a+(n-1)d$ (correct)
  • $T_n = a+(n+1)d$
  • $T_n = a+(n-1)/d$
  • $T_n = a-(n-1)d$
  • What is the general formula for finding the sum of the first n terms in an arithmetic sequence?

  • $S_n = 2(a+l)$
  • $S_n = n(a+l)$
  • $S_n = 2n(2a+(n-1)d)$
  • $S_n = n(2a+(n-1)d)$ (correct)
  • What defines a geometric sequence?

  • Each term is found by adding a constant to the preceding term.
  • Each term is found by multiplying the preceding term by a fixed number. (correct)
  • Each term is obtained by subtracting a constant from the preceding term.
  • Each term is obtained by dividing the preceding term by a fixed number.
  • What is the formula for finding the nth term in a geometric sequence?

    <p>$T_n = ar^{n-1}$</p> Signup and view all the answers

    What is the formula for finding the sum of the first n terms in a geometric sequence?

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

    Under what condition does an infinite geometric series exist?

    <p>$|r| &lt; 1$</p> Signup and view all the answers

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