Consider sequences consisting of three non-zero real numbers.
a. (i) State the necessary and sufficient condition for numbers x,y,z to be consecutive terms of an arithmetic progression and of a geometric progression, respectively.
b. (ii) Decide whether the triple −6,−2,2 forms an arithmetic progression, a geometric progression, or neither. Show complete justification.
c. (iii) Prove that the only sequence which can simultaneously be an arithmetic progression and a geometric progression is the constant sequence in which all terms are equal.