Question

find the common ratio and write out the first four terms of the geometric sequence \\(\frac{3^{n+1}}{7}\\)

common ratio is

\\(a_1 =\\) , \\(a_2 =\\) , \\(a_3 =\\) , \\(a_4 =\\)

Explanation:

Step1: Identify the general term formula

$$a_n = \frac{3^{n+1}}{7}$$

Step2: Calculate the first term

$$a_1 = \frac{3^{1+1}}{7} = \frac{9}{7}$$

Step3: Calculate the second term

$$a_2 = \frac{3^{2+1}}{7} = \frac{27}{7}$$

Step4: Calculate the third term

$$a_3 = \frac{3^{3+1}}{7} = \frac{81}{7}$$

Step5: Calculate the fourth term

$$a_4 = \frac{3^{4+1}}{7} = \frac{243}{7}$$

Step6: Determine the common ratio

$$r = \frac{a_2}{a_1} = \frac{\frac{27}{7}}{\frac{9}{7}} = 3$$

Answer:

Common ratio is \(3\)
\(a_1 = \frac{9}{7}\), \(a_2 = \frac{27}{7}\), \(a_3 = \frac{81}{7}\), \(a_4 = \frac{243}{7}\)