2024 IGCSE Additional Mathematics October/November 0606/21 Q12

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 \(a_{100}=b_1=298\).

1. Find \(n\) such that \(a_n-b_n=45\).[6]
2. Find the smallest \(m\) such that \(a_m>2b_m\).[3]