
Arithmetic series is the sum of an arithmetic sequence. Example: a) 3 + 7 + 11 + 13 + 15 + ......... + 99 b) 5 + 10 + 15 + 20 + ................+ 2000 Method 1: Example: Find the sum of the series 3 + 7 + 11 + 13 + 15 + ......... + 99 First write the sum twice, one in an ordinary order and the other in a reverse order: By adding vertically, each pair of numbers adds up to 102: S = 3 + 7 + 11 + 13 + 15 + ......... ......+ 99 +S = 99 + 95 + 91 + 87 + .......................3  2S = 102 + 102 + 102 + 102 + 102 + 102 + 102 Therefore S = (102 + 102 + 102 + 102 + 102 + 102 + 102)/ 2 To find out how many number of terms in the series we have to find n a_{1} = 3 d = 4 a_{n} = a_{1} + (n1)d = 99 3 + (n1)x4 = 99 3 + 4n  4 = 99 4n  1 = 99 4n = 100 n = 25 Since there are 25 of these sums of 102 2S = 102 + 102 + 102 + 102 + 102 + 102 + 102 2S = 25 x 102 S = (25x102)/2 S = 1275 Directions: Find the sum of the arithmetic series below. Also write at least 5 examples of your own. 