Question

find the common ratio and write out the first four terms of the geometric sequence \\((1.02)^{n-1}\\)

common ratio is
\\(a_1 =\\)
\\(a_2 =\\)
\\(a_3 =\\)
\\(a_4 =\\)

Explanation:

Step1: Identify the common ratio

$$r = 1.02$$

Step2: Calculate the first term

$$a_1 = (1.02)^{1-1} = 1$$

Step3: Calculate the second term

$$a_2 = (1.02)^{2-1} = 1.02$$

Step4: Calculate the third term

$$a_3 = (1.02)^{3-1} = 1.0404$$

Step5: Calculate the fourth term

$$a_4 = (1.02)^{4-1} = 1.061208$$

Answer:

Common ratio is \(1.02\)
\(a_1 = 1\)
\(a_2 = 1.02\)
\(a_3 = 1.0404\)
\(a_4 = 1.061208\)