Question

Consecutive terms of a sequence have the values 2, -1, 1/2 , - 1/4 , and 1/8 . Of the following, which describes the sequence?

A. The terms could be part of a geometric sequence with a common ratio of —2.
B. The terms could be part of a geometric sequence with a common ratio of - 1/2 .
C. The terms could be part of a geometric sequence with a common ratio of 1/2 .
D. The terms are part of a sequence other than a geometric sequence because the common ratio of a geometric sequence must be positive.

Answer 1

The sequence provided is a geometric sequence with a common ratio of -1/2, as each term is -1/2 times the previous term, making option B the correct answer.

Step-by-step explanation:

The consecutive terms of the sequence are 2, -1, 1/2, -1/4, and 1/8. To determine if this is a geometric sequence and to find the common ratio, we look at the ratio of each term to its predecessor. For example:

Term 2 to Term 1: (-1)/2 = -1/2

Term 3 to Term 2: (1/2)/(-1) = -1/2

Term 4 to Term 3: (-1/4)/(1/2) = -1/2

Term 5 to Term 4: (1/8)/(-1/4) = -1/2

Since the ratio between successive terms is consistently -1/2, the sequence is a geometric sequence with a common ratio of -1/2. Hence, the terms could be part of a geometric sequence with a common ratio of -1/2, which corresponds to option B.

Answer 2

The sequence 2, -1, 1/2, -1/4, 1/8 is a geometric sequence with a common ratio of -1/2, which corresponds to option B.

Step-by-step explanation:

You want to determine if the sequence 2, -1, 1/2, -1/4, and 1/8 is a geometric sequence and, if so, what the common ratio is. A geometric sequence is one where each term after the first is found by multiplying the previous term by a fixed non-zero number, called the common ratio.

To find the common ratio, we divide each term by the term that precedes it:

• -1 ÷ 2 = -1/2
• 1/2 ÷ -1 = -1/2
• -1/4 ÷ 1/2 = -1/2
• 1/8 ÷ -1/4 = -1/2

The common ratio is consistently -1/2. Therefore, the correct answer to the question is B. The terms could be part of a geometric sequence with a common ratio of -1/2.