If one or more unsuccessful attempts at personal service are made by the sheriff or deputy upon a conservator or guardian appointed in this state at the last known address of the conservator or guardian that appears in the court records and it appears to the court that further attempts are likely to be futile, then service shall be sufficient upon the conservator or guardian if the citation is mailed by first-class mail to the last known address of the conservator or guardian.
OCGA § 29-9-6