Gr12 Mathematics: Ch 1.5 Finite Arithmetic Series

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Questions and Answers

What is the condition for the sum of an infinite geometric series to exist?

  • r < -1
  • r = 0
  • -1 < r < 1 (correct)
  • r > 1

What happens when the common ratio r is greater than or equal to 1?

  • The series converges
  • The series is undefined
  • The series equals zero
  • The series diverges (correct)

What is the formula for the sum of an infinite geometric series?

  • S∞ = a / (1 - r) (correct)
  • S∞ = a + r
  • S∞ = a(1 - r)
  • S∞ = ar

What happens when the common ratio r is less than or equal to -1?

<p>The series diverges (D)</p> Signup and view all the answers

What is an infinite geometric series?

<p>A series where the number of terms goes to infinity (B)</p> Signup and view all the answers

If the common ratio r is 0.5, what can be concluded about the infinite geometric series?

<p>The series is convergent (C)</p> Signup and view all the answers

What is the value of the sum of an infinite geometric series if the first term is 2 and the common ratio is 0.75?

<p>8 (D)</p> Signup and view all the answers

If an infinite geometric series has a common ratio of -0.8, what can be said about the series?

<p>The series is convergent (A)</p> Signup and view all the answers

What is a necessary condition for an infinite geometric series to be convergent?

<p>The common ratio is between -1 and 1 (B)</p> Signup and view all the answers

If an infinite geometric series has a common ratio of 1.2, what can be concluded about the series?

<p>The series is divergent (D)</p> Signup and view all the answers

What is the range of values for the common ratio r such that the infinite geometric series is divergent?

<p>$r \leq -1$ or $r \geq 1$ (C)</p> Signup and view all the answers

If the sum of an infinite geometric series exists, which of the following statements is true?

<p>The common ratio r must be greater than -1 and less than 1. (B)</p> Signup and view all the answers

What can be concluded about an infinite geometric series if the common ratio r is -0.4?

<p>The series is convergent. (A)</p> Signup and view all the answers

Which of the following is a characteristic of a convergent infinite geometric series?

<p>The series has a sum that is always finite. (C)</p> Signup and view all the answers

What is the relationship between the sum of an infinite geometric series and the common ratio r?

<p>The sum increases as the absolute value of r increases. (D)</p> Signup and view all the answers

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