Gr12 Mathematics: Ch 1.5 Finite Arithmetic Series

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?

The series diverges Signup and view all the answers

What is an infinite geometric series?

A series where the number of terms goes to infinity Signup and view all the answers

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

The series is convergent 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?

8 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?

The series is convergent Signup and view all the answers

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

The common ratio is between -1 and 1 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?

The series is divergent 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?

$r \leq -1$ or $r \geq 1$ Signup and view all the answers

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

The common ratio r must be greater than -1 and less than 1. Signup and view all the answers

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

The series is convergent. Signup and view all the answers

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

The series has a sum that is always finite. Signup and view all the answers

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

The sum increases as the absolute value of r increases. Signup and view all the answers

Gr12 Mathematics: Ch 1.5 Finite Arithmetic Series

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