0606 P21 - Nov 2024 - Q12 - 9 marks
7250
Two arithmetic progressions, \(A\) and \(B\), each have 100 terms. Their terms are denoted by \(a_{1}, a_{2}, a_{3}, a_{4}, \ldots a_{100}\) and \(b_{1}, b_{2}, b_{3}, b_{4}, \ldots b_{100}\) respectively.
It is given that \(a_{1}=b_{100}=1\) and \(a_{100}=b_{1}=298\). (a) Find \(n\) such that \(a_{n}-b_{n}=45\). (b) Find the smallest \(m\) such that \(a_{m}\gt 2 b_{m}\).
