334 ^^' Rotheram onjome Properties 



mainder ix\ as will appear by the operation ; 

 1xr-\-%xr ^ +2Arr% &c.)2*' + 2A:r * + 2A-r * + 2;fr*, &c.( 

 r, in the quotient nxr^-\-^xr'' ■\-%xr^ ^hz. 



■2.x * * * thie re- 



mainder. 



Hence this general Rule. Divide the fum of 



the fquares by the fum of the feries. Add the 



quotient to, and fubtradt it from, the fum 



of the feries. Divide the greater of thefe 



two numbers by the lefs ; the quotient of this 



fecond divifion fhall be the common ratioj and 



the remainder twice the firft term. 



Example I. Let ^ = 242, and ^ = 29524. 

 Then— =122, and 242 + 122 = 364, and 242— 

 122 = 120 ; and 364 divided by 120, gives 3 in 

 the quotient, for the common ratio, and 4 in 

 the remainder, the half of which, 2, for the firft 

 term of the feries. And, thefe being known, the 

 number of terms will be found by the common 

 rules. Whence the feries is 2, 6, 18, 54, 162. 



Example II. Let (3=68887 and ^= 237 2950489; 

 then — = 34447, and a +— = 103334, which di- 

 vided by a — -= 34440, gives, in the quotient, 

 3 for the common ratio, and in the remainder 

 14, the half of which, 7, for the firft term 1 

 whence the feries is 7, 21, 6^3 189, &c. to 9 

 places. 



Example 



