An arithmetic progression (AP) with first term a and common difference d and a geometric progression (GP) with the same first term a and common ratio r are both non-constant. If their 3rd terms are equal and their 5th terms are also equal, which of the following statements is correct?
a) They exist only when r=−1.
b) They exist whenever r2=2.
c) No such pair of non-constant sequences exists.
d) They exist only when d=0.