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. $\(\frac\)34,\(\frac\)12,\(\frac\)13,\(\frac\)29,\(\ldots\)$
• C. $\(\frac\)34,2,\(\frac\)83,\(\frac{32}{9}\),\(\ldots\)$
• D. $\(\frac\)23,\(\frac\)12,\(\frac\)38,\(\frac{9}{32}\),\(\ldots\)$

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 the \(n\)th term of a geometric sequence is given by the formula: \(a_n = a_1 \times r^{n-1}\).
3. Calculate the second term \(a_2\) by substituting \(n=2\) into the formula: \(a_2 = a_1 \times r^{2-1} = a_1 \times r\).
4. Calculate the third term \(a_3\) by substituting \(n=3\): \(a_3 = a_1 \times r^{3-1} = a_1 \times r^2\).
5. Calculate the fourth term \(a_4\) by substituting \(n=4\): \(a_4 = a_1 \times r^{4-1} = a_1 \times r^3\).