i6S iEiTKMtTlC* 



5. What is tlic riintli root of 21035-8 ? 



Ans. 3'02223i> 



ARITHMETICAL PROGRESSION. 



Any rank of numbers increasing by a common excess, 

 or c^ecreniring by a common difference, are said to be in 

 j^rithnctical Progression ; such are the numbers i, 2, 3, 4, 

 ,5, &c. 7, 5, 3, I •, and '8, '6, 'zi, '2. When the numbers 

 increase they fofm an asce?iding scries ; but v/hcn they de- 

 crease, they form a descending series. 



The numbers, which forrii the series, are called the terms 

 cf the progression; 



Any three of the five following terms being given, the 

 other two may be readily found. 



1. Tiie first term, 7 commonly called the 



2. The hst termt,- 3 extremes* 



3. The number of terms. 



4- The comm.on difference. 



5- The sum of all the terms, 



PROBLITM I. 



*Thc first iernty the last term^ and the number of terms lacing 

 given, to find the siwi of all the terms. 



RULE.* 



Multiply the sum of the extremes by the number of 

 terms, and Iralf the product will be the answer. 



EXAAIPLIZS. 



* Suppose another series of the same kind with the given one 

 be placed under. it in" an inverse order ; then ulll the sum of every 

 two corLesponding terms be the same as that of the first and last ; 



consequently, 



