Final answer:
The client is experiencing neuropathic pain due to their amputated arm. The brain still receives pain signals from the nerves that used to be connected to the amputated limb, causing sensations such as throbbing or burning.
Step-by-step explanation:
The client is experiencing neuropathic pain. Neuropathic pain occurs as a result of damage or dysfunction in the nervous system. In the case of the client with an amputated arm, the brain may still receive pain signals from the nerves that used to be connected to the amputated arm, leading to sensations such as throbbing or burning in the absent limb.