Infinite Geometric Series Quiz

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

• The ratio must be less than one.

• The series must have an even number of terms.

• The first term must be zero.

• The ratio must be greater than one.

What is a convergent series?

• A series that has no sum.

• A series with a ratio greater than one.

• A series that diverges to infinity.

• A series that converges to a specific number.

In a divergent series, what happens to the sum of the terms?

• It approaches zero.

• It remains constant.

• It becomes negative.

• It increases without bound.

How do you determine the common ratio of a geometric series?

• Divide the second term by the first term.

• Multiply the first term by the second term.

• Divide the first term by the second term.

• Add the first and second terms.

If the common ratio of a series is 5/2, what can be said about the series?

• It converges.

• It diverges.

• It is not a geometric series.

• It has a sum of zero.

What is the formula for the sum of a convergent infinite geometric series?

• First term multiplied by (1 + ratio)

• First term divided by (1 - ratio)

• First term divided by (1 + ratio)

• First term multiplied by (1 - ratio)

If the first term of a series is 4 and the ratio is 0.5, what is the sum of the series?

• 4

• 8

• 16

• 2

What is the common ratio if each term is multiplied by 1/4?

• 1/3

• 1/2

• 1/5

• 1/4

If a series has a common ratio of 6/5, what can be concluded?

• The series converges.

• The series diverges.

• The series has a sum of zero.

• The series is not geometric.

What should you do to determine if a series converges or diverges?

• Multiply all terms by two.

• Check if the first term is zero.

• Find the common ratio and check if it is less than one.

• Ensure the series has an even number of terms.