Arithmetic Progression And Geometric Progression Gmat, Gre Problem

The second, the first and the third term of an Arithmetic Progression  whose common difference is non zero but lesser than 200, form a Geometric Progression in that order. What is the common ration of that Geometric Progression?

A. 1
B. -1+
C. 2
D. -2
E. |1|





Let the 3 terms of the AP be (a-d), a and (a+d)
Terms of the GP: a, (a-d), (a+d) in that order.
In a GP, terms next to each other have the same ratio.
So, (a−d)a=(a+d)(a−d)$\frac{(a-d)}{a}=\frac{(a+d)}{(a-d)}$

(a−d)2=a(a+d)$(a-d{)}^2=a(a+d)$

d2−2ad=ad$d^2-2ad=ad$

d2−3ad=0$d^2-3ad=0$

d(d−3a)=0$d(d-3a)=0$

We know that d is not 0 from the question. So d = 3a

Common ratio =(a−d)a=(a−3a)a=−2$=\frac{(a-d)}{a}=\frac{(a-3a)}{a}=-2$