Write the first four terms of the following geometric sequence.
$a_1=\frac{3}{4},r=\frac{2}{3}$

• A. $\frac{3}{4},\frac{1}{2},\frac{3}{8},\frac{9}{32},\dots$
• B. $\frac{3}{4},\frac{1}{2},\frac{1}{3},\frac{2}{9},\dots$
• C. $\frac{3}{4},2,\frac{8}{3},\frac{32}{9},\dots$
• D. $\frac{2}{3},\frac{1}{2},\frac{3}{8},\frac{9}{32},\dots$

Answer: (B)

Verified step by step guidance

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