MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Two arithmetic progressions are given.
Progression P: 2, 5, 8, 11, …
Progression Q: 3, 7, 11, 15, …
Answer the following:
(i) Determine whether there is a term that is common to both progressions and does not exceed 200. If such a term exists, find the smallest one.
(ii) For the term found in part (i), state its position number in each progression.
(iii) If no such term exists, provide algebraic justification for the absence of a common term up to 200.