Exploring Geometric Sequences

What is a sequence in mathematics?

• A collection of random numbers.

• A progression of numbers.

• A group of even numbers.

• A set of unrelated numbers.

In a geometric sequence, what is the term used for the fixed multiple between successive numbers?

• Common factor

• Common ratio

• Common product

• Common difference

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the third term?

• 162

• 54

• 18

• 6

What is the main difference between a sequence and a series?

• A sequence is a progression of numbers, while a series is a sum of a sequence.

• A sequence is always arithmetic, while a series is not.

• A sequence is a sum of numbers, while a series is a progression of numbers.

• A sequence is always geometric, while a series is not.

What is a geometric series?

• A sequence of numbers with a common difference.

• A sum of a geometric sequence.

• A product of a geometric sequence.

• A sequence of numbers with a common ratio.

In the bungee jumping problem, what is the common ratio for the rope stretch?

• 0.5

• 0.6

• 0.7

• 0.4

What is the formula for the stretch on the nth bounce in the bungee jumping problem?

• 120 * 0.6^(n+1)

• 120 * 0.6^(n-1)

• 120 * 0.6^(n+2)

• 120 * 0.6^n

How much does the rope stretch on the 12th bounce in the bungee jumping problem?

• 0.56 feet

• 0.36 feet

• 0.26 feet

• 0.46 feet

Why is it important to match the value of n with the correct term in a sequence?

• To ensure the sequence is geometric.

• To ensure the calculations are accurate.

• To ensure the sequence is arithmetic.

• To ensure the sequence is finite.

What happens to the rope stretch after the 12th bounce in the bungee jumping problem?

• It stops completely.

• It decreases to about 3 inches.

• It remains the same.

• It increases significantly.