k + 4, 4k-2, 7k + 1 are in G.P.

\(\frac{4k−2}{k+4}=\frac{7k+1}{4k−2}\)

∴ (4k-2) (4k- 2) = (7k + 1) (k + 4)

∴ 16k^{2} – 16k + 4 = 7k^{2} + 28k + k + 4

∴ 16k^{2} – 7k^{2} – 16k – 28k – k + 4 – 4 = 0

∴ 9k^{2} – 45k = 0

∴ 9k (k – 5) = 0

∴ 9k = 0

OR

k – 5 = 0

∴ k = 0 OR k = 5

Numbers are positive. Hence, k = 5