Understanding Infinite Geometric Series

The video tutorial explains how to find the infinite sum of a geometric sequence, given the first term and common ratio. It highlights that the infinite sum exists only if the absolute value of the common ratio is less than one. The tutorial provides a step-by-step calculation of an infinite sum for a sequence with a common ratio of 3/4, resulting in a sum of 96. It also presents an example where the infinite sum does not exist due to a common ratio greater than one, illustrating the terms growing indefinitely. The video concludes with a brief mention of the next example to be covered in a subsequent video.

What is the condition for the existence of an infinite sum in a geometric series?

• The absolute value of the common ratio must be greater than 1.

• The absolute value of the common ratio must be less than 1.

• The common ratio must be less than 1.

• The common ratio must be greater than 1.

If the first term of a geometric series is 24 and the common ratio is 3/4, what is the infinite sum?

• 96

• 120

• 72

• 48

How do you calculate the infinite sum of a geometric series?

• Multiply the first term by the common ratio.

• Multiply the first term by 1 minus the common ratio.

• Divide the first term by the common ratio.

• Divide the first term by 1 minus the common ratio.

What is the second term in the series with a first term of 24 and a common ratio of 3/4?

• 16

• 12

• 24

• 18

What is the third term in the series with a first term of 24 and a common ratio of 3/4?

• 10.5

• 13.5

• 9

• 18

Why does the infinite sum not exist for a series with a first term of 2 and a common ratio of 3?

• The terms oscillate.

• The terms decrease to zero.

• The terms remain constant.

• The terms increase indefinitely.

What happens to the terms of a geometric series when the common ratio is greater than 1?

• They decrease to zero.

• They remain constant.

• They increase indefinitely.

• They oscillate.

In the example with a first term of 2 and a common ratio of 3, what is the second term?

• 4

• 8

• 10

• 6

In the example with a first term of 2 and a common ratio of 3, what is the third term?

• 12

• 18

• 15

• 21

What is the key takeaway regarding the sum of an infinite geometric series?

• The sum exists only if the absolute value of the common ratio is less than 1.

• The sum exists only if the common ratio is positive.

• The sum exists only if the common ratio is negative.

• The sum always exists.