Answer the following questions about arithmetic and geometric progressions.
a. (a) State the defining condition for a sequence to be an arithmetic progression and the defining condition for a sequence to be a geometric progression.
b. (b) Explain, with reasoning, whether a non-constant sequence can satisfy both conditions simultaneously.
c. (c) Give one explicit example of an arithmetic progression and one explicit example of a geometric progression, each having first term 4, and justify why each example meets the respective defining condition.