Let A ={1,2,3, …., 100} and R be a relation on A such that R ={( a, b ): a =2 b +1}. Let ( a_1.,. a_2),( a_2, a_3),( a_3, a_4), ….,( a_k, a_k +1 ) be…

Let $\displaystyle \mathrm{A}=\{1,2,3, \ldots ., 100\}$ and R be a relation on A such that $\displaystyle \mathrm{R}=\{(\mathrm{a}, \mathrm{b}): \mathrm{a}=2 \mathrm{~b}+1\}$. Let $\displaystyle \left(\mathrm{a}_1\right.$, $\displaystyle \left.\mathrm{a}_2\right),\left(\mathrm{a}_2, \mathrm{a}_3\right),\left(\mathrm{a}_3, \mathrm{a}_4\right), \ldots .,\left(\mathrm{a}_{\mathrm{k}}, \mathrm{a}_{\mathrm{k}+1}\right)$ 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: