2025 RI P1 Q6

A finite arithmetic progression \(A\) has \(n\) terms, first term \(a\) and common difference \(d\). In another progression \(B\), the \(k\)th term is obtained by adding the \(k\)th positive odd integer to the corresponding term of \(A\). That is, the first term of \(B\) is obtained by adding \(1\) to the first term of \(A\), the second term of \(B\) is obtained by adding \(3\) to the second term of \(A\) and so on. It is given that the twelfth term of \(A\) is \(25\), the sum of all the terms of \(A\) is \(676\) and the sum of all the terms of \(B\) is twice the sum of all the terms of \(A\).