I didn't come up with this problem, but I still think it's a good one.

There are 4 positive integers in order from least to greatest, such that the first three make an aritmetic sequence, and the last three make a geometric sequence. If the difference between the largest and smallest term is 30, what are the terms?

I like this problem very much, as it is simple to state but challenging to solve. It is not difficult to show that the geometric factor must be less than 2. With a little experimentation, one can derive a set on numbers that meets the problem's requirements. These are 18, 27, 36 and 48. The first three are arithmetic with a delta of 9. The last three are geometric with a factor of 3/2 times the previous term. The last temr is 30 more than the first. Gordon S.

Posted by Gordon Steel on 2003-09-24 19:42:12