what are the first three terms of a geometric sequence in which (a_{5}=25) and the common ratio is…

Explanation:

Step1: Recall geometric - sequence formula

The formula for the (n)th term of a geometric sequence is (a_n=a_1r^{n - 1}), where (a_n) is the (n)th term, (a_1) is the first - term, (r) is the common ratio, and (n) is the term number. Given (a_5 = 25) and (r = 5), we substitute into the formula: (a_5=a_1r^{5 - 1}), so (25=a_1\times5^{4}).

Step2: Solve for (a_1)

We have the equation (25=a_1\times625). To find (a_1), we divide both sides of the equation by 625: (a_1=\frac{25}{625}=\frac{1}{25}).

Step3: Find the second term (a_2)

The formula for the second term is (a_2=a_1r). Substituting (a_1=\frac{1}{25}) and (r = 5), we get (a_2=\frac{1}{25}\times5=\frac{1}{5}).

Step4: Find the third term (a_3)

The formula for the third term is (a_3=a_2r). Since (a_2=\frac{1}{5}) and (r = 5), we have (a_3=\frac{1}{5}\times5 = 1).

Answer:

A. (\frac{1}{25},\frac{1}{5},1)