Infinite Geometric Series Quiz

What is a geometric sequence?

• A sequence where each term is multiplied by a constant.

• A sequence where each term is added by a constant.

• A sequence where each term is subtracted by a constant.

• A sequence where each term is divided by a constant.

If the first term of a geometric sequence is 4 and the common ratio is 3, what is the third term?

• 9

• 12

• 108

• 36

How do you find the nth term of a geometric sequence?

• Multiply the first term by the common ratio raised to the power of n.

• Add the first term to the common ratio raised to the power of n.

• Multiply the first term by the common ratio raised to the power of n minus one.

• Divide the first term by the common ratio raised to the power of n minus one.

What condition must be met for an infinite geometric series to converge?

• The common ratio must be less than 1.

• The common ratio must be equal to 1.

• The common ratio must be negative.

• The common ratio must be greater than 1.

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

• First term divided by 1 minus the common ratio.

• First term multiplied by 1 minus the common ratio.

• First term multiplied by the common ratio.

• First term divided by the common ratio.

If the first term of an infinite geometric series is 3 and the common ratio is 1/4, what is the sum of the series?

• 4

• 3

• 12

• 1

In the series 3^n * 3 / 4^n, what is the common ratio?

• 1/3

• 1/4

• 4/3

• 3/4

What is the value of r that makes the series 17r^0 / (1-r) equal to 23?

• 6/23

• 23/6

• 6/20

• 20/23

When using a calculator to solve series problems, why is it important not to round intermediary steps?

• It ensures the final answer is accurate.

• It simplifies the calculations.

• It makes the process faster.

• It is not important.

What is the approximate sum of the series with the first term 0.1429 and common ratio 0.52285?

• 1.2995

• 0.1429

• 0.2995

• 0.52285