Question

The common ratio of G.P.: \(25, -5, 1, -\frac{1}{5}, \dots\) is:

• A. \(-\frac{1}{5}\)
• B. \(\frac{1}{5}\)
• C. \(2 \, \frac{5}{5}\)
• D. \(\frac{3}{5}\)

Hint:

To find the common ratio of a G.P., divide any term by the preceding term. If the result is constant, that is the common ratio.

Answer 1

The Correct Option is A

The common ratio \(r\) in a geometric progression is found by dividing any term by the previous term. For the given G.P. \(25, -5, 1, -\frac{1}{5}, \dots\), the common ratio is: \[ r = \frac{-5}{25} = -\frac{1}{5} \] Thus, the correct answer is option (1).