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reciprocate (v.)

1610s, "to give and return mutually," a back-formation from reciprocation, or else from Latin reciprocatus, past participle of reciprocare "rise and fall, move back and forth; reverse the motion of," from reciprocus "returning the same way, alternating" (see reciprocal). Sense of "cause to move back and forth" is from 1650s; intransitive sense of "move backward and forward" is from 1670s. Meaning "to give or do in response, act in return or response" is from 1820. Related: Reciprocated; reciprocating.

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Definitions of reciprocate from WordNet

reciprocate (v.)
act, feel, or give mutually or in return;
We always invite the neighbors and they never reciprocate!
reciprocate (v.)
alternate the direction of motion of;
the engine reciprocates the propeller
From wordnet.princeton.edu