Variable bandwidth channels can be created in Flexible Grid Optical Networks using Optical Orthogonal Frequency Division Multiplexing (O-OFDM). This allows more efficient use of spectrum by allocating integral multiple of basic bandwidth slot to the lightpath requests. In these networks, the constraint of keeping all the allocated slots together is added when deciding the routes for the requests. This constraint is called the contiguity constraint, which makes the routing and spectrum arrangement algorithms more challenging. In any network, the lightpath requests will arrive and depart dynamically and invariably lead to spectrum fragmentation. Hence network will have to reduce the maximum possible utilization as well as increased blocking probability. In this paper, we have presented an improvised Routing and Spectrum Assignment (RSA) algorithm using consecutive spectrum slots that leads to lesser fragmentation. It is evident from the results that the presented RSA algorithm uses adaptive parameters to reduce the blocking probability and fragmentation compared to the other algorithms reported in the recent past.