Question 979914


If you want to calculate the sum of all integers from  52  to  122


52 + 53 + . . . + 122,


then note that it is the sum of terms of an arithmetic progression.


The first term of this progression is  52,  the common difference is  1,  and the number of terms is  122 - 51 = 71. 


So, &nbsp;you can apply the formula for the sum of arithmetic progression &nbsp;(see, &nbsp;for example, &nbsp;the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>&nbsp; in this site) 


{{{S}}} = {{{((a[1] + a[n])*n)/2}}} = {{{(52 + 122)*71/2}}} = 6177.