Question

If \(k\), 6 and \(k+5\) are the first three terms of a geometric series, then the possible values of the common ratio are

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

Hint:

Always check both roots of the quadratic equation. In G.P. problems, a negative value for \(k\) is perfectly valid and leads to an alternating series.

Answer 1

The Correct Option is D