Exploring Arithmetic and Geometric Sequences

What defines an arithmetic sequence?

• None of the above

• Dividing by a constant number

• Adding or subtracting a constant term

• Multiplying by a constant ratio

How do you find the nth term in an arithmetic sequence?

• Start with the first term and add the common difference (n-1) times

• Multiply the first term by n

• Subtract the common difference from the last term n times

• Add the common difference to the first term n times

What is the common difference in the given arithmetic sequence?

• 3

• -3

• 2

• -2

What characterizes a geometric sequence?

• None of the above

• Constant addition or subtraction

• Constant division

• Multiplying by a common ratio

How is the nth term of a geometric sequence calculated?

• Adding the first term to the common ratio raised to the power of n-1

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

• Multiplying the first term by the common ratio raised to the power of n-1

• Dividing the first term by the common ratio raised to the power of n-1

What is the common ratio in the provided geometric sequence?

• 2

• -2

• -3

• 3

Why is the exponent n-1 used in the explicit rule for geometric sequences?

• To compensate for the first term being a part of the sequence

• To adjust for the starting index of sequences

• Because you multiply the first term by the common ratio starting from the second term

• It represents the number of terms minus the first term

How does a recursive rule differ from an explicit rule?

• It defines each term based on the previous term

• It requires knowledge of all previous terms

• It only applies to arithmetic sequences

• It calculates each term independently

What is the first step in constructing a recursive rule for an arithmetic sequence?

• Identify the common ratio

• Define the first term

• Calculate the common difference

• Multiply the first term by the common difference

In a geometric sequence recursive rule, what operation is performed to find the next term?

• Addition

• Subtraction

• Division

• Multiplication