Three numbers a , b and c are in geometric progression. If 4 a , 5 b and 4 c are in arithmetic progression and a + b + c = 70 , then the value of c - a is equal to

Step-by-step solution

a + b + c = 7 0 ⇒ a + a r + a r 2 = 7 0 Also, 10 b = 4 a + 4 c ⇒ 10 a r = 4 a + 4 a r 2 ⇒ 2 r 2 - 5 r + 2 = 0 ⇒ r = 2 , 1 2 For r = 2 , we have, a 1 + r + r 2 = 70 ⇒ a = 70 1 + r + r 2 = 70 1 + 2 + 4 = 1 0 ⇒ a = 10 ,   b = 20 ,   c = 40 ⇒ c - a = 3 0 For r = 1 2 , we have, a = 70 1 + r + r 2 = 70 1 + 1 2 + 1 4 = 70 × 4 4 + 2 + 1 = 4 0 ⇒ b = 20 ,   c = 1 0 ⇒ c - a = 10 - 40 = 3 0 So, in both the cases c - a = 30