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>$T_n = ar^{n-1}$ (D)</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>$S_n = a(1-r^n)/(1-r)$ (B)</p> Signup and view all the answers

Under what condition does an infinite geometric series exist?

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

Flashcards

nth term in arithmetic sequence

T_n = a + (n - 1)d, where a is the first term and d is the common difference.

Sum of first n terms in arithmetic sequence

S_n = n(2a + (n - 1)d), where n is the number of terms.

Geometric sequence definition

A sequence where each term is found by multiplying the previous term by a fixed number, called the common ratio.

nth term in geometric sequence

T_n = ar^(n - 1), where a is the first term and r is the common ratio.

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Sum of first n terms in geometric sequence

S_n = a(1 - r^n) / (1 - r), valid for r not equal to 1.

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Condition for infinite geometric series

An infinite geometric series exists if |r| < 1, ensuring convergence.

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