find the value of k so that k-3,k+1,4k-2 form a geometric sequence.

Answer 1

to form a GS, the square of the middle term must equal to product of the outer terms

(k+1)^2 = (k-3)(4k-2)
k^2 + 2k + 1 = 4k^2 - 14k + 6
3k^2 - 16k + 5 = 0
(k - 5)(3k - 1) = 0
k = 5 or k = 1/3