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?

shorter:

d(n-1) = 10.5
(dn)/2 = 6

divide one eq. by another:  n/(n-1)=7/8

       so n=8, d=1.5 etc