Answer the following questions about arithmetic and geometric progressions.
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Answer the following questions about arithmetic and geometric progressions.
(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) Explain, with reasoning, whether a non-constant sequence can satisfy both conditions simultaneously.
(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.