The first four terms of an arithmetic sequence are: a, a + d, a + 2d, a + 3d. The first four terms of another sequence are: A, Ar, Ar2, Ar3, where r 6= 1. The eight terms

satisfy:

a + A = 27 (1)

(a + d) + (Ar) = 27 (2)

(a + 2d) + (Ar2) = 39 (3)

(a + 3d) + (Ar3) = 87 (4)

By using the substitution a = 27 − A, or otherwise, find the all eight terms