Problem:
Suppose x,y,z is a geometric sequence with common ratio r and xî€ =y. If x,2y,3z is an arithmetic sequence, then r is
Answer Choices:
A. 41​
B. 31​
C. 21​
D. 2
E. 4
Solution:
Since y=xr,z=xr2 and 3z−2y=2y−x, by substitution
3xr2−2xr=2xr−x or 3r2−4r+1=0
Thus (3r−1)(r−1)=0. Since xî€ =y, it follows that rî€ =1. Thus r=1/3.