Question

Let three numbers a, b, c between 2 and 18 be such that
(1) Their sum is 25,
(2) The number 2,a,b are in A.P and
(3) The numbers b, c, 18 are in G.P. Find c

• A. 13
• B. 12
• C. 10
• D. 15

Answer 1

The correct option is B 12

a + b + c = 25 ............................. (1)

2a = 2+b => b = (2a - 2) ........ (2)

c² =18b ................................... (3)

From the above equations,

a + (2a - 2) + (18b)^1/2= 25

{3a - 2} + {36(a - 1)}^1/2 = 25

3a + 6(a - 1)^1/2 = 27

a + 2(a - 1)^1/2 = 9

a = 5, b = 8 and c = 12