Exploring Arithmetic and Geometric Sequences

What defines an arithmetic sequence?

• A sequence where each term is multiplied by a constant

• A sequence where each term is divided by a constant

• A sequence with a common ratio

• A sequence with a common difference

What is the common difference in the sequence 4, 7, 10, 13?

• 5

• 4

• 2

• 3

What characterizes a geometric sequence?

• A sequence with a common ratio

• A sequence with a common difference

• A sequence where each term is subtracted by a constant

• A sequence where each term is added by a constant

If a geometric sequence has terms 10, 20, 40, 80, what is the common ratio?

• 1/2

• 10

• 5

• 2

How do you find the next term in a geometric sequence?

• Add the common difference to the last term

• Divide the last term by the common ratio

• Subtract the common difference from the last term

• Multiply the last term by the common ratio

What is the next term in the arithmetic sequence 29, 31.5, 34, 36.5?

• 38

• 39

• 39.5

• 40

How can you identify an arithmetic sequence from a formula?

• It includes a minus sign

• It includes a plus sign

• It includes a division sign

• It includes a multiplication sign

What is required to create your own geometric sequence?

• A common ratio

• A common difference

• A starting number and a common ratio

• A starting number and a common difference

In the context of sequences, what does 'r' typically represent?

• The common difference

• The starting number

• The number of terms

• The common ratio

What is the purpose of using summation notation in sequences?

• To find the common difference

• To identify the type of sequence

• To calculate the sum of a certain number of terms

• To determine the next term