Variable bandwidth channels can be created in Flexible Grid Optical Networks using Optical Orthogonal Frequency Division Multiplexing (O-OFDM). This allows more efficient spectrum use by allocating integral multiple of basic bandwidth slots to the lightpath requests. In these networks, the constraint of keeping all the allocated slots together is added when deciding routes for the requests. This makes the Routing and Spectrum Assignment (RSA) algorithms in Flexible Grid Optical Networks more challenging. In any network, the lightpath requests will arrive and depart dynamically, leading to spectrum fragmentation. It leads to a reduction of maximum possible utilization as well as an increase in blocking probability. In this paper, we have presented an improvised RSA algorithm using consecutive spectrum slots as an adaptive parameter, that leads to reduced fragmentation. It is evident from the results that the presented RSA algorithm using adaptive parameters reduces the blocking probability and fragmentation more effectively than the shortest path and k-shortest path algorithms reported in the earlier works.