ARITHMETICAL PROGRESSION, l6^ 



EXAMPLES. 



I. The first term of an arithmetical progression is 2, 

 the last term 53, and the number of terms 18 ; required the 

 yum of the series. 



53 



55 

 18 



440 

 55 



2)990 



495 



Or, 



53 + 2x18 , 



^•^-i =495 "^^ answer. 



2. The first term is i, the last term 21, and the numbct 

 of terms 1 1 , required the sum of the series. 



Ans. 121. 



3. How many strokes do the clocks of Venice, which 

 go to 24 o'clock, strike in the compass of a day ? 



Ans. 300. 



4. If 



consequently, any one of those sums, multiplied by the number of 

 terms, must give the whole sum of the two series, and half that 

 sum will evidently be the sum of the given series : thus, 



Let I, 2, 3, 4, 5, 6, 7, be the given series ; 

 and 7, 6, 5, 4, 3, 2, i, the same inverted ; 

 then 8 + 8 + 84.8 + 8 + 84-8=8x7=56and 1+3+4+5 



+ 6+7=1?= 28. Q: E. D. 



