Question

If a, b, care in A.P. b – a, c – b and a are in G.P., then a : b : c is

• A. 1 : 2 : 3
• B. 1 : 3 : 5
• C. 2 : 3 : 4
• D. 1 : 2 : 4

Answer 1

Answer: (A)

1 : 2 : 3

Answer 2

Given, a, b, c are in A.P. ⇒ 2b = a + c

b – a, c – b, a are in G.P. So $( c - b ) ^ { 2 } = a ( b - a )$

⇒ $( b - a ) ^ { 2 } = ( b - a ) a$ $\left[ \begin{array} { l l } \because & 2 b = a + c \\ \Rightarrow & b + b = a + c \\ \Rightarrow & b - a = c - b \end{array} \right]$

⇒ $b = 2 a$ [∵ b ≠ a]

Put in 2b = a + c, we get c = 3a. Therefore a : b : c = 1 : 2 : 3