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### High School Mathematics - 23.3 Sum of an Arithmetic Series

 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 a1 = 3 d = 4 an = a1 + (n-1)d = 99 3 + (n-1)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.
 Q 1: If the first term is 10, the common difference is 3 and the number of terms is 20. Find the sum of the terms in the series. (Hint: Here a1=10, d=3, n=20 Find S)700770690 Q 2: (-5)+(-3)+(-1)+1+3+......+51667690789 Q 3: Find the sum of the first 8 terms of the series: 4+7+10+13+... 100112150 Q 4: 22+42+62+82 +......+1002 - (12+32+52+72+......992) (Hint: 22-12=3, 42-32= 7 and so on....)245660905050 Q 5: Find the sum of the series: 3 + 7 + 11 + 15 + ... + 35 200171210 Q 6: Find the sum of the series: 1+2+3+4+5+........100404050507077 Q 7: Find the sum of the first 30 terms of series: 5 + 9 + 13 + 17 + . . . 231418901670 Q 8: Find the sum of 8 + 5 + 2 + .......+ (-10)-12-13-7 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!