A sequence is defined by the general term an=pn+q, where p and q are real constants and n≥1.
a. (a) Prove that the sequence {an} is an arithmetic progression.
b. (b) Conversely, let {bn} be any arithmetic progression with first term b1 and common difference d. Prove that bn can be expressed in the form bn=pn+q, and identify p and q in terms of b1 and d.