Either a ward, on arriving at the age of majority, or a new guardian legally appointed may apply to the judge of the probate court for an order requiring the original guardian or his personal representative to appear and submit to a settlement of his accounts. The citation shall be served as are other citations and shall be returnable to a regular term of the court. If the guardian fails or refuses to appear as cited, the court may proceed without the appearance of the guardian. If the guardian has been required to give bond, the surety on such bond shall be bound by the settlement if the surety is given notice by personal service of the settlement proceeding in the probate court. If one or more unsuccessful attempts at service are made by the sheriff or his deputy upon the guardian at the last address of the guardian in the court records and it appears to the judge of the probate court that further attempts are likely to be futile, then service shall be sufficient upon the guardian for purposes of this Code section if the citation is mailed by first-class mail to such address.