Let \(A={1,2,3,\ldots .,100}\) and \(R\) be a relation on \(A\) such that \(R={(a,b):a=2b+1}\). Let \(\left({a}_{1},{a}_…

Let \(A={1,2,3,\ldots .,100}\) and \(R\) be a relation on \(A\) such that \(R={(a,b):a=2b+1}\). Let \(\left({a}_{1},{a}_{2}\right)\), \(\left({a}_{2},{a}_{3}\right),\left({a}_{3},{a}_{4}\right),\ldots .,\left({a}_{k},{a}_{k+1}\right)\) be a sequence of \(k\) elements of \(R\) such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer \(k\), for which such a sequence exists, is equal to: