Three students made the following claims about arithmetic progressions: A: “If the…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Three students made the following claims about arithmetic progressions:
A: “If the first three terms of a sequence are 4, 7, and 11, it is an AP because the third term exceeds the first by 7.”
B: “In any AP, the sum of the first and third terms equals twice the second term only when the common difference is 2.”
C: “A sequence with a common difference 0 is not an AP because the terms do not change.”
Analyse the validity of each claim.
(i) For each claim A, B, and C, state whether the claim is correct or incorrect. Provide a clear mathematical justification for your decision.
(ii) Rewrite every incorrect claim in a correct mathematical statement that accurately reflects the properties of arithmetic progressions.