\']0 ARITHMETIC, 



4. It 100 Stones be placed in a right line, exactly a yard 

 asunder, and tlic fu'st a. yard from. a basket, what length of 

 ground will that man go, who gathers them up shigly, re- 

 turning with them one by one to the basket ? , 



Ans. 5 miles and 1300 yards. 



PROBLEM II. 



T/jd first ierWi the last terniy av.cl the tiumher of terms being 

 giveiiy to find the commsn. difference, 



RULE.* , 



Divide the difference of the extremes by the number of 

 terms less i, and the quotient will be the common differ- 



ence sought. 



EXAMPLES. 



I. The extremes are 2 and 53, and the number of terraa 

 is 1 3 ; required the common difference. 



53 

 2 



17)51(3 17 



51 



Or, 



53—2 Kl ,, 



^^ — zz - — zr 1, the answer. 



i8~i 17 ^ 



2. If 



* The difference ofthe first and last terms evidently shews the 

 Increase of the first term by all the subsequent additions, till it 

 becomes equal to the last ; and as the number of those additions 

 is evidently one less than the number of terms, and the increase 

 by every addition equal, it is plain, that the total increase, divided 

 by the number of additions, must give the difference at every one 

 separately ; whence the rule is manifest. 



