reciprocate
v.v. to do something for someone because they did something for you first. It is like saying 'I will do the same for you'.
v. to perform an action in return for a previous one; to give or do something in return. Often used in the context of social obligations or physical actions.
I will reciprocate your kindness by helping you tomorrow.
After the host invited her for dinner, she felt she should reciprocate by hosting a small gathering in return.
In many traditional societies, the failure to reciprocate a gift or a favor is viewed as a serious social slight, potentially damaging the trust between two families.
From Latin recīprocātus, perfect passive participle of recīprocō (“to move back and forth”) (see -ate (verb-forming suffix)), from reciprocus (“back an forth, reciprocal, alternating”) + -ō (first conjugation verb-forming suffix), itself possibly from a phrase such as reque proque (“back and forth”), from re- (“back”), prō (“forwards”) and -que (“and”). See also reciprocal. Compare French réciproquer.