Richard, listed below shows why I gave you the other census, LDS, and rootsweb information.
1910 census is Luther and Rosie with Luther's mother Sarah.
1900 census is Luther with his mother Sarah.
1880 census is Luther's father Benjamin and his mother Sarah.
1870 census is Benjamin with his father William M and his mother Nancy.
The rootsweb listing shows Benjamin married to Sarah Green and his father and his mother as Nancy Vann.
The LDS shows William Cook married to Nancy Vane.
I hope this explanation helps.I was trying to give you more generations before Luther Benjamin.
LDS WILLIAM COOK Male Event(s):Birth: Christening: Death: Burial: Marriages:Spouse:NANCY VANE Marriage:20 MAY 1841, Wilkinson, Georgia
http://worldconnect.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=:3164202&id=I185http://worldconnect.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=:3164202&id=I185 ID: I185 Name: Benjamin COOK Sex: M Birth: Abt 1852 in Wilkinson,Georgia Note: BIOGRAPHY: Occupation: Farmer Change Date: 23 FEB 2003 at 10:37:11 Father: William COOK b: 1809 in Georgia Mother: Nancy VANN b: Abt 1813 in Wilkinson,Georgia Marriage 1 Sarah GREEN b: in Georgia Married: 21 APR 1874 in Gadsden,Florida Children Bryant Wilbur COOK b: 3 APR 1884 Oscar COOK b: 13 APR 1879 in Georgia Luther COOK Mary COOK Mattie COOK
Home in 1870:Griffin, Wilkinson, Georgia Name:Wm M Cook Age in 1870:60 Birth Year:abt 1810 Birthplace:Georgia Race:White Gender:Male Household Members: NameAge Wm M Cook60 Farmer Nancy Cook46 Wife GA Martha Cook24 Daughter GA Amos Cook20 Son GA Benjamin Cook17 Son GA Hampton Cook16 Son GA Joel A Cook12 Son GA Doctor Cook7 Son GA Arthur O Cook5 Son GA
Home in 1880:District 332, Wilkinson, Georgia Name:Benjamin Cook Age:28 Birth Year:abt 1852 Birthplace:Georgia Race:White Gender:Male Relation to Head of House:Self (Head) Marital Status:Married Spouse's Name:Sarah Cook Father's Birthplace:Georgia Mother's Birthplace:Georgia Occupation:Farmer Household Members: NameAge Benjamin Cook28 Sarah Cook28 Wife GAGAGA Oscar Cook1 Son GAGAGA
Home in 1900:Griffin, Wilkinson, Georgia Name:Sarah S Cook Age:48 Birth Date:May 1852 Birthplace:Georgia Race:White Gender:Female Relation to Head of House:Head Marital Status:Widowed Father's Birthplace:Georgia Mother's Birthplace:Georgia Mother: number of living children:6 Mother: How many children:6 Occupation:Farmer Household Members: NameAge Sarah S Cook48 Oscar F Cook21 Son Apr 1879 Luther B Cook19 Son Nov 1880 Leah Vastie Cook17 Daughter Jan 1883 Briant W Cook16 Son Apr 1884 Mary Esther Cook11 Daughter Sep 1888 Mattie Cook9 Daughter Jan 1891
Home in 1910:Milan, Telfair, Georgia Name:Mrs Sarah S Cook Age in 1910:57 Birth Year:1853 Birthplace:Georgia Race:White Gender:Female Relation to Head of House:Head [Self (Head)] Marital Status:Widowed Father's Birthplace:Georgia Mother's Birthplace:Georgia Household Members: NameAge Mrs Sarah S Cook57 Farmer General Farm Owns Luthur Cook29 Son Physician Practitioner Married 1 time 0 years Rosa Lee Cook24 Daughter-in-law Married 1 time 0 years Mattie D Cook17 Daughter