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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
3.3 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: (-5)+(-3)+(-1)+1+3+......+51
690
667
789

Q 2: Find the sum of 8 + 5 + 2 + .......+ (-10)
-13
-7
-12

Q 3: Find the sum of the series: 3 + 7 + 11 + 15 + ... + 35
210
171
200

Q 4: Find the sum of the first 30 terms of series: 5 + 9 + 13 + 17 + . . .
1890
2314
1670

Q 5: 1+4+7+10+13+16+.........+100
1717
1990
2319

Q 6: 22+42+62+82 +......+1002 - (12+32+52+72+......992) (Hint: 22-12=3, 42-32= 7 and so on....)
6090
5050
2456

Q 7: Find the sum of the first 8 terms of the series: 4+7+10+13+...
100
112
150

Q 8: 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)
700
690
770

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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