Write the first four terms of the following geometric sequence.
$a_1=-8,r=-\frac{1}{2}$

• A. $-8,4,-2,1,\dots$
• B. $-8,-\frac{17}{2},-9,-\frac{19}{2},\dots$
• C. $-8,\frac{1}{4},-\frac{1}{2},1,\dots$
• D. $-\frac{1}{2},4,-32,256,\dots$

Answer: (A)

Verified step by step guidance

1. Identify the first term \(a_1\) and the common ratio \(r\) of the geometric sequence. Here, \(a_1 = -8\) and \(r = -\frac{1}{2}\).
2. Recall that each term in a geometric sequence is found by multiplying the previous term by the common ratio \(r\). The formula for the \(n\)-th term is \(a_n = a_1 \times r^{n-1}\).
3. Calculate the second term \(a_2\) by multiplying the first term by \(r\): \(a_2 = a_1 \times r = -8 \times \left(-\frac{1}{2}\right)\).
4. Calculate the third term \(a_3\) by multiplying the second term by \(r\): \(a_3 = a_2 \times r\).
5. Calculate the fourth term \(a_4\) by multiplying the third term by \(r\): \(a_4 = a_3 \times r\).