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

Let \(\mathrm{A}={1,2,3,\ldots .,100}\)and R be a relation on A such that \(\mathrm{R}={(\mathrm{a},\mathrm{b}):\mathrm{a}=2\mathrm{b}+1}\). Let \(\left({\mathrm{a}}_{1},{\mathrm{a}}_{2}\right)\), \(\left({\mathrm{a}}_{2},{\mathrm{a}}_{3}\right),\left({\mathrm{a}}_{3},{\mathrm{a}}_{4}\right),\ldots .,\left({\mathrm{a}}_{\mathrm{k}},{\mathrm{a}}_{\mathrm{k}+1}\right)\) 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 :