If the KH,2k_1 and 3k are those conservative. Term of a gp find the value of the common ratio

Answer 1

The common ratio (r) of a geometric progression (GP) can be found by dividing any term by its previous term.

The given terms of the GP are KH, 2k_1, and 3k.

To find the common ratio, divide the second term by the first term:
r = (2k_1) / KH

To find the common ratio, divide the third term by the second term:
r = (3k) / (2k_1)

Since the common ratio of a geometric progression is the same regardless of which terms are divided, we can set the two expressions equal to each other:
(2k_1) / KH = (3k) / (2k_1)

Cross-multiplying:
(2k_1)(2k_1) = (3k)(KH)
4k_1^2 = 3kKH

Dividing both sides by 3k:
(4k_1^2) / (3k) = KH

Simplifying:
(4k_1 / 3) = KH

Therefore, the common ratio of the geometric progression is (4k_1 / 3).