An arithmetic series is a sum of numbers which change by repeated addition. An example:<\/p>\n
5+11+17+23+….+143<\/p>\n
The question posed might be as follows:<\/p>\n
Find the sum of the arithmetic series 5+11+17+23+….+143.<\/strong><\/p>\n Solution:<\/p>\n A formula for the sum is<\/p>\n Sn<\/sub>=n(t1<\/sub>+tn<\/sub>)\/2<\/p>\n where<\/p>\n t1<\/sub> is the first term<\/p>\n tn<\/sub> is the last term<\/p>\n n is the number of terms.<\/p>\n Note that while, in our case, t1<\/sub>=5 and tn<\/sub>=143, we don’t yet know n.<\/p>\n However, we can use the term formula<\/p>\n tn<\/sub>=t1<\/sub>+d(n-1)<\/p>\n in which d is the amount added to get the next term; in our case, d=6.<\/p>\n We can find n as follows:<\/p>\n 143=5+6(n-1)<\/p>\n which becomes<\/p>\n 138=6(n-1)<\/p>\n Next, dividing both sides by 6, we get<\/p>\n 23=n-1<\/p>\n n=24<\/p>\n Apparently 143 is the 24th term. Now, to find the sum of 5+11+17+23+….+143, we can use<\/p>\n Sn<\/sub>=n(t1<\/sub>+tn<\/sub>)\/2<\/p>\n as follows:<\/p>\n S24<\/sub>=24(5+143)\/2=24(148)\/2=12(148)=1776<\/p>\n Apparently, 5+11+17+23+….+143=1776:)<\/p>\n Source:<\/p>\n Travers, Kenneth J. et al. Using Advanced Algebra<\/i>. Toronto: Doubleday Canada, 1977.<\/p>\n