Exploring Geometric Sequences and Exponential Functions

What is a geometric sequence?

• A list of numbers without any specific order

• A list of numbers where each term is divided by a constant

• A list of numbers where each term is multiplied by a constant

• A list of numbers where each term is added by a constant

How do you find the common ratio in a geometric sequence?

• By subtracting consecutive terms

• By multiplying consecutive terms

• By adding consecutive terms

• By dividing any term by its preceding term

What is the next term in a sequence with a common ratio of 1/3, starting from 1/3?

• 2/3

• 1/9

• 1/6

• 1

What is the common ratio if the sequence starts with -4 and the next term is 16?

• -4

• 4

• -0.25

• 0.25

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

• 12

• 9

• 24

• 6

How is a geometric sequence expressed as an exponential function?

• a_n = a_1 * r^(n-1)

• a_n = a_1 + r^(n-1)

• a_n = a_1 / r^(n-1)

• a_n = a_1 - r^(n-1)

What is the 10th term of a sequence starting with 96 and a common ratio of 0.5?

• 0.09375

• 0.1875

• 192

• 48

What distinguishes a geometric sequence from an arithmetic sequence?

• Use of division to find the next term

• Use of multiplication to find the next term

• No specific method to find the next term

• Use of addition to find the next term

Which of the following is not a sequence?

• 3, 6, 12, 24

• 5, 10, 20, 40

• 2, 4, 8, 16

• 4, 9, 12, 18

Which sequence is an example of an arithmetic sequence?

• -20, -15, -10, -5

• 1, 2, 4, 8

• 10, 20, 40, 80

• 5, 10, 15, 25