Understanding Geometric Sequences

What is the main difference between geometric and arithmetic sequences?

• Both sequences are defined by a common ratio.

• Geometric sequences have a common ratio, while arithmetic sequences have a common difference.

• Arithmetic sequences have a common ratio.

• Geometric sequences have a common difference.

In a geometric sequence, what does the term 'common ratio' refer to?

• The sum of all terms in the sequence.

• The first term of the sequence.

• The difference between consecutive terms.

• The ratio of any two consecutive terms.

Given the sequence 1, 10, 100, 1000, what is the common ratio?

• 1000

• 1

• 10

• 100

If the first term of a geometric sequence is 1 and the common ratio is 10, what is the fifth term?

• 1000

• 100000

• 10000

• 100

In a geometric sequence where the first term is 5 and the common ratio is 3, what is the third term?

• 60

• 15

• 30

• 45

How do you find the sixth term in a geometric sequence with a first term of 5 and a common ratio of 3?

• Add 3 to the first term five times.

• Multiply the first term by 3 five times.

• Multiply the first term by 3 raised to the power of 5.

• Add 5 to the first term three times.

What is the value of the sixth term in the sequence where the first term is 5 and the common ratio is 3?

• 729

• 1215

• 243

• 3645

Which of the following is NOT a characteristic of a geometric sequence?

• It involves multiplication or division.

• It has a common difference.

• It has a common ratio.

• The terms grow exponentially.

What is the formula to find the nth term in a geometric sequence?

• a + (n-1)d

• a * r^(n-1)

• a + r^(n-1)

• a * n^r

If a geometric sequence has a first term of 2 and a common ratio of 4, what is the fourth term?

• 256

• 128

• 64

• 32