Final answer:
First order neurons of the dorsal columns project to the nucleus gracilis and nucleus cuneatus in the brainstem, where they synapse with second order neurons and later ascend to the thalamus and cerebral cortex.
Step-by-step explanation:
The first order neurons of the dorsal columns, which are part of the somatosensory pathway that carries information regarding touch, proprioception, and vibration senses, project to specialized nuclei located in the brainstem. Specifically, these neurons terminate in the nucleus gracilis for the lower body and leg fibers (fasciculus gracilis), and the nucleus cuneatus for the upper body and arm fibers (fasciculus cuneatus).
Once there, they synapse with the second order neurons. Following this, the second order neurons decussate to the opposite side and ascend as the medial lemniscus to synapse with the third order neurons in the thalamus. Eventually, these sensations reach the cerebral cortex for processing.