Question

The second and third terms of a G.P is 6 times the fourth term. Find the possible values of the common ratio. ​

Answer 1

-1/3 or 1/2.

Explanation:

Second term = ar, the third = ar^2 and the fourth = ar^3.

So we have the equation:

ar + ar^2 = 6ar^3

r + r^2 = 6r^3

6r^3 - r^2 - r = 0

r(6r^2 - r - 1) = 0

(3r + 1 )(2r -1) = 0

r = -1/3, 1/2.