Problem:
If a,b,c,d are positive real numbers such that a,b,c,d form an increasing arithmetic sequence and a,b,d form a geometric sequence, then da is
Answer Choices:
A. 121
B. 61
C. 41
D. 31
E. 21
Solution:
We have b=a+r,c=a+2r, and d=a+3r, where r is a positive real number. Also, b2=ad yields (a+r)2=a(a+3r), or r2=ar. It follows that r=a and d=a+3a=4a. Hence da=41.
The problems on this page are the property of the MAA's American Mathematics Competitions