Answer : To find: Value of k

Given: k + 12, k – 6 and 3 are in GP

Formula used: (i) when a,b,c are in GP b2 = ac As, k + 12, k – 6 and 3 are in GP

⇒ (k – 6)2 = (k + 12) (3)

⇒ k2 – 12k + 36 = 3k + 36

⇒ k2 – 15k = 0

⇒ k (k – 15) = 0

⇒ k = 0 , Or k = 15

Ans) We have two values of k as 0 or 15