Arithmetic and Geometric Progressions Quiz
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Arithmetic and Geometric Progressions Quiz

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Questions and Answers

What defines an arithmetic progression?

  • A sequence with a variable difference between terms.
  • A sequence where terms increase or decrease by a constant number. (correct)
  • A sequence where terms are multiplied by a constant.
  • A sequence that comprises only prime numbers.

    • Which formula represents the nth term of an arithmetic progression?

  • $a_n = ar^{n - 1}$
  • $a_n = \frac{n}{2}(2a + (n - 1)d)$
  • $a_n = a + (n - 1)d$ (correct)
  • $a_n = a\frac{1 - r^n}{1 - r}$

    • What is the common ratio in a geometric progression?

  • The constant ratio by which terms are multiplied. (correct)
  • The sum of the first and second terms.
  • The difference between consecutive terms.
  • The product of the first and last terms.

    • Which of the following sums represents the sum of the first n terms of a geometric progression?

    <p>$S_n = a\frac{1 - r^n}{1 - r}$</p> Signup and view all the answers

    If the first term of an arithmetic progression is 5 and the common difference is 3, what is the 4th term?

    <p>14</p> Signup and view all the answers

    What is the value of the first term in a geometric progression if $a = 2$, and the common ratio $r = 3$?

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

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