The number of terms of an Arithmetic Progression is even.

The sum of the terms in the odd places (First term + Third Term + Fifth Term + ...and so on) is 24;

The sum of the terms in the even places (Second Term + Fourth Term + Sixth Term + ... and so on) is 30; and

The last term exceeds the first by 21/2, then:

What is the arithmetic progression?

The number of terms is given to be even.  However, that did not need to be required -- it can be proved form the other specifications.  If the terms are a, a+d, ..., a+2nd then the odd places sum to (n+1)(a+nd)=24 and the even places sum to n(a+nd)=30 so that (n+1)/n=24/30 which is impossible.

Posted by Richard on 2006-03-23 13:25:20