V!6 



ARITHMETIC. 



EXAMPLES. 



I. The first term of a series- in geometrical progression 

 is I, the htt term is 2187, and the ratio 3 5 wkit is the' 

 sum of the series ? 



2187 



65 6 T 



3 — 'i::-z2)6^6o 



3280 



dr, 



3X218 7 1__ 



3280 the answer. 



2. The 



Note i. Since, in any geometrical series or progression, when 

 it consists of four terms, the product of the extremes is equal to 

 the product of the means ; and when it consists of three, the 

 product of the extremes is equal to the square of the mean ; it 

 follows, that in any geonjietrical series, when it consists of. an even 

 number of terms, the product of the extremes is equal to the 

 product of any two means, equally distant from the extremes ; 

 and, when the number of terms is odd, the product of the ex~ 

 jtremes is equal to the square of the mean or middle term, or to 

 the product of any two terms equally distant from them. 



Note 2. If 



Then <! 



a 

 a 

 h 



a—b 



la^b 



h 



c 



a 



b 



b 



a-\-b 



a~b 



c : 

 h : 

 d : 



c—d 



: c 



d directly^ 

 d by alternation. 

 c by inversion. 

 : d by composition. 

 : d by division, 

 : c-\'d h'j conversion. 



c-^-d 



mixedly. 



For in each of these proportions the product of the extremes is 

 equal to that of tlic means. 



