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?

(In reply to guess by Bry)

For the first three terms to be in arithmetic sequence would require the difference between the first two terms to be the same as the difference between the second and third terms, which is not the case here.

For the last three terms to be in geometric sequence the ratio of the last term to the next to last would have to be the same as that between the next to last and the one before it, which is also not the case in 60, 65, 80, 90.

Posted by Charlie on 2003-09-23 20:58:51