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)
∴ 16k2 – 16k + 4 = 7k2 + 28k + k + 4
∴ 16k2 – 7k2 – 16k – 28k – k + 4 – 4 = 0
∴ 9k2 – 45k = 0
∴ 9k (k – 5) = 0
∴ 9k = 0
OR
k – 5 = 0
∴ k = 0 OR k = 5
Numbers are positive. Hence, k = 5