Exploring Geometric Sequences

What is the common ratio in a geometric sequence?

• The common ratio is the constant factor between consecutive terms.

• The common ratio is the average of all terms in the sequence.

• The common ratio is the difference between consecutive terms.

• The common ratio is the sum of consecutive terms.

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the second term?

• 4

• 9

• 12

• 6

Calculate the 5th term of the geometric sequence where the first term is 4 and the common ratio is 3.

• 324

• 81

• 108

• 12

What is the formula for the nth term of a geometric sequence?

• a_n = a_1 * n * r

• a_n = a_1 + r^(n-1)

• a_n = r^(n-1)

• a_n = a_1 * r^(n-1)

If a geometric sequence has a first term of 5 and a common ratio of 0.5, what is the 4th term?

• 2.5

• 1.25

• 10

• 0.625

Determine the sum of the first 6 terms of a geometric sequence with a first term of 2 and a common ratio of 3.

• 216

• 728

• 486

• 364

In a geometric sequence, if the 3rd term is 12 and the 5th term is 48, what is the common ratio?

• 2

• 6

• 4

• 3

How do you find the sum of an infinite geometric series?

• S = a / (1 - r) for |r| < 1

• S = a + r for |r| < 1

• S = a / r for |r| > 1

• S = a * (1 - r) for |r| < 1

If the first term of a geometric sequence is 10 and the common ratio is -2, what is the 3rd term?

• -20

• 30

• 100

• 40

What is the relationship between the terms of a geometric sequence and their common ratio?

• The terms of a geometric sequence are always equal to each other.

• The common ratio varies between the terms of a geometric sequence.

• The terms of a geometric sequence are related by a constant common ratio.

• The terms of a geometric sequence are determined by their sum.