1. Tardigrade
  2. Question
  3. Mathematics
  4. If a, b, c are three unequal numbers such that a, b, c are in A.P. and b - a, c - b, a are in G.P., then a: b: c is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If a, b, c are three unequal numbers such that a, b, c are in A.P. and b - a, c - b, a are in G.P., then a : b : c is

Sequences and Series

Solution:

Since $a, b, c$ are in $A.P$.
$\therefore b - a = c - b $
Also $b - a, c - b, a$ are in $G.P$.
$\therefore (c-b)2 = (b-a)a$
$ \Rightarrow (b - a)^2 = (b - a)a$
$\Rightarrow b - a = a$
$\Rightarrow b = 2a$
Also $c = 2b - a = 2(2a) - a = 3a$
$\therefore a : b : c = a : 2 a : 3a = 1 : 2 : 3$