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The first term of a geometric sequence is -2 and the common ratio is [tex]\(-\frac{1}{4}\)[/tex]. What are the next three terms of the sequence?

A. [tex]\(-\frac{1}{2}, -\frac{1}{8}, -\frac{1}{32}\)[/tex]
B. [tex]\(\frac{1}{2}, -\frac{1}{8}, -\frac{1}{32}\)[/tex]
C. [tex]\(-\frac{1}{2}, \frac{1}{8}, -\frac{1}{32}\)[/tex]
D. [tex]\(\frac{1}{2}, \frac{1}{8}, \frac{1}{32}\)[/tex]



Answer :

GinnyAnswer
To determine the next three terms of the geometric sequence with the given first term and common ratio, we will follow these steps:

1. Identify the first term and the common ratio:
- First term ([tex]\(a_1\)[/tex]) = -2
- Common ratio ([tex]\(r\)[/tex]) = -[tex]\(\frac{1}{4}\)[/tex]

2. Calculate the second term ([tex]\(a_2\)[/tex]):
- [tex]\(a_2 = a_1 \times r = -2 \times -\frac{1}{4}\)[/tex]
- [tex]\(a_2 = \frac{1}{2}\)[/tex]

3. Calculate the third term ([tex]\(a_3\)[/tex]):
- [tex]\(a_3 = a_2 \times r = \frac{1}{2} \times -\frac{1}{4}\)[/tex]
- [tex]\(a_3 = -\frac{1.}{8}\)[/tex]

4. Calculate the fourth term ([tex]\(a_4\)[/tex]):
- [tex]\(a_4 = a_3 \times r = -\frac{1}{8} \times -\frac{1}{4}\)[/tex]
- [tex]\(a_4 = \frac{1}{32}\)[/tex]

So, the next three terms of the sequence would be:
[tex]\[ \frac{1}{2}, -\frac{1}{8}, \text{ and } \frac{1}{32} \][/tex]

Let's match these with the provided answer choices:
- [tex]\(-\frac{1}{2},-\frac{1}{8},-\frac{1}{32}\)[/tex]
- [tex]\(\frac{1}{2},-\frac{1}{8}, \cdot \frac{1}{32}\)[/tex]
- [tex]\(-\frac{1}{2}, \frac{1}{8},-\frac{1}{32}\)[/tex]
- [tex]\(\frac{1}{2}, \frac{1}{8}, \frac{1}{32}\)[/tex]

The correct set of next three terms is:
[tex]\[ \frac{1}{2}, -\frac{1}{8}, \frac{1}{32} \][/tex]

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