Understanding Geometric Sequences

What is the common ratio in a geometric sequence?

• The common ratio is the difference between consecutive terms.

• The common ratio is the average of the first and last terms.

• The common ratio is the sum of consecutive terms.

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

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

• 9

• 6

• 12

• 4

Which of the following is a geometric sequence?

• 2, 6, 18, 54

• 1, 3, 5, 7

• 4, 8, 12, 16

• 5, 10, 15, 20

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

• a_n = a_1 + r^(n-1)

• a_n = a_1 * r^(n-1)

• a_n = a_1 * n * r

• a_n = r^(n-1)

If the third term of a geometric sequence is 24 and the common ratio is 3, what is the first term?

• 18

• 6

• 12

• 8/3

In a geometric sequence, if the first term is 5 and the fifth term is 405, what is the common ratio?

• 5

• 2

• 10

• 3

How do you find the sum of the first n terms of a geometric sequence?

• S_n = a * r^n for r ≠ 1

• S_n = a * n^2 for all r

• S_n = a + r * n for r = 1

• S_n = a(1 - r^n) / (1 - r) for r ≠ 1; S_n = n * a for r = 1.

If a geometric sequence has a first term of 1 and a common ratio of 1/2, what is the fourth term?

• 1

• 1/4

• 1/8

• 1/2

Which of the following statements is true about geometric sequences?

• In a geometric sequence, each term is found by multiplying the previous term by a constant ratio.

• The ratio between consecutive terms in a geometric sequence varies randomly.

• Geometric sequences can only contain positive numbers.

• In a geometric sequence, each term is found by adding a constant value to the previous term.

If the second term of a geometric sequence is 10 and the common ratio is 5, what is the first term?

• 2

• 5

• 15

• 50