Question

If k 1,2k-1,3k 1 are three consecutive terms of a geometric progression. find the possible values of the common ratio

a) 3/2
b) 3/2
c) 2
d) 3

Answer 1

To find the common ratio of the geometric progression, we equate the ratios of consecutive terms, solve for k, and then calculate the common ratio.

Step-by-step explanation:

The question asks about finding the common ratio of a geometric progression with given consecutive terms that follow the pattern: k, 2k-1, and 3k+1. In a geometric progression (GP), the ratio between any two consecutive terms is constant. Therefore, the ratio between the second term (2k-1) and the first term (k) should be the same as the ratio between the third term (3k+1) and the second term (2k-1).

We set up two ratios to represent this:

1. (2k-1)/k = r
2. (3k+1)/(2k-1) = r

By equating the two expressions for r, we can solve for k and subsequently find the common ratio:

(2k-1)/k = (3k+1)/(2k-1)

Cross-multiplying and solving for k gives us k/(2k-1), which can then be substituted back into either of the initial equations to get the common ratio.