172 



ARITHMETIC. 



EXAMPLES. 



I. The extremes are 2 and 53, and the common diiFcr- 

 ence 3 ; what is the number of terms ? 

 53 



3)51 

 I 



18 



Or, 



3J. J- 1 = 18 the answer. 



2. If 



That is, if 1,3, 5, 7, 9, &c. be the numbers, 

 Then will i, 2^, 3*, 4*, 5^, &c. be the sums of i, 2, 3, &c^ 

 of those terms. 



For, o-f-i or the sum of i term = i* or i 

 I -}- 3 or the sum of 2 terms = 2 * or 4 

 4-J-5 or the sum of 3 terms = 3* or 9 

 94-7 or the sum of 4 terms = 4^ or 16, &c. 

 Whence it is plain, that, let n be any number whatsoever, the 

 £um of n terms v/iil be n^. 



The following table contains a summary of the whole doctrine 

 of arithmetical progression. 



Cases of Jujthmetjcal Progression. 



Case;Giv. | Req. 



r" 

 / 



adn 



Solution. 



n — I xd-^-a. 



2 



Case 



