Answer:
1144
Step-by-step explanation:
100 + 98 + 96 +.... + 78+76 =
(12-0)/2 (176)
(6.5) (176) = 1144
The sum of the series will be 1068.
We have the following expression -
[tex]\sum_{i=0}^{12} 100 - 2i[/tex]
We have to rewrite the series as the sum.
A series in mathematics is the sum of a list of numbers that are generated according to some pattern.
We have the following expression -
[tex]\sum_{i=0}^{12} 100 - 2i[/tex]
The terms of this series can be calculated by calculating the value of the function at different values of i.
The series is as follows -
100 + 98 + 96 +.... + 78+76
This is an arithmetic progression with a = 100 and d = - 2 and n = 12. The sum of this series is -
[tex]S = \frac{n}{2} \times {2a + (n-1)d}[/tex]
S = [tex]\frac{12}{2} [{2 \times 100 + (12 -1)(-2)] = 6[200+ 11 \times -2] = 6[200 -22][/tex]
S = 6 x 178 = 1068
The sum of the series will be 1068.
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