Understanding Geometric Sequences and Common Ratios

What distinguishes a geometric sequence from an arithmetic sequence?

• Arithmetic sequences involve division by a constant.

• Geometric sequences have a common difference.

• Arithmetic sequences have a common ratio.

• Geometric sequences involve multiplication by a constant.

How is the common ratio of a geometric sequence determined?

• By multiplying all terms together.

• By dividing a term by its preceding term.

• By adding the first and last terms.

• By subtracting the first term from the last term.

Why is it important to verify the common ratio in a geometric sequence?

• To determine the sequence's length.

• To confirm the sequence is geometric.

• To find the sum of the sequence.

• To ensure the sequence is arithmetic.

What is the common ratio in the sequence: 3, 9, 27, 81?

• 4

• 3

• 2

• 5

If a sequence alternates between negative and positive terms, what can be inferred about the common ratio?

• The common ratio is greater than one.

• The common ratio is negative.

• The common ratio is zero.

• The common ratio is positive.

How do you express a common ratio when a sequence is decreasing?

• As a decimal greater than one.

• As a negative number.

• As a whole number.

• As a fraction less than one.

What is the common ratio of the sequence: 2/9, 1/3, 2/3?

• 1/2

• 1/3

• 2/3

• 3/2

How do you find the common ratio in a sequence involving decimals?

• By multiplying the decimals.

• By dividing one decimal by the previous one.

• By subtracting the decimals.

• By adding the decimals.

What is the common ratio of the sequence: 0.2, 0.26, 0.338?

• 1.1

• 1.3

• 1.2

• 1.5

Why might a calculator be useful when finding the common ratio of a sequence with decimals?

• To add the decimals accurately.

• To perform long division more easily.

• To multiply the decimals quickly.

• To subtract the decimals correctly.