Question

x + y + z = 15. If 9,x,y,z,a  are in AP, while 1/x + 1/y + 1/z = 5/3 If 9, x, y, z, a are in HP. Then the value of a will be

(A)  1

(B)  2 

(C)  3 

(D)  9 

Answer 1

Correct option (A) 1

x + y + z = 15. If 9,x,y,z,a  are in AP, then

Sum = 9 + 15 + a = 5/2(9 + a) ⇒ 24 + a = 5/2(9 + a)

⇒ 48 + 2a = 45 + 5a ⇒ 3a = 3 ⇒ a = 1  ....(1)

and 1/x + 1/y + 1/z = 5/3. If 9,x, y, z ,a are in HP, then