Three numbers a , b and c are in between 2 and 18 such that 2 , a , b are in arithmetic progression and b , c , 18 are in geometric progression. If a + b + c = 25 , then the value of c - a is

Step-by-step solution

a + b + c = 25 ; 2 a = 2 + b ; c 2 = 18 b ⇒ 2 a + 2 b + 2 c = 5 0 ⇒ 2 + b + 2 b + 2 c = 5 0 ⇒ 3 b + 2 c = 48 ⇒ c 2 6 + 2 c = 4 8 ⇒ c 2 + 12 c - 48 × 6 = 0 ⇒ c 2 + 12 c - 24 × 12 = 0 ⇒ c + 24 c - 12 = 0 ⇒ c = 12 , - 24 ⇒ c = 1 2 (between 2 and 18 ) ⇒ b = c 2 18 = 144 18 = 8 ⇒ a = b + 2 2 = 5 ⇒ a = 5 ,   b = 8 and c = 12 ⇒ c - a = 7