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The sum of the first 50 positive even integers is 2550. What
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01 Jul 2020, 09:55
01 Jul 2020, 09:55
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The sum of the first 50 positive even integers is 2550. What is the sum of even integers from 102 to 200 inclusive?
A. 5,100
B. 7,550
C. 10,100
D. 15,500
E. 20,100
A. 5,100
B. 7,550
C. 10,100
D. 15,500
E. 20,100
Re: The sum of the first 50 positive even integers is 2550. What
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01 Jul 2020, 09:55
01 Jul 2020, 09:55
Expert Reply
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Re: The sum of the first 50 positive even integers is 2550. What
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01 Jul 2020, 10:23
01 Jul 2020, 10:23
1
Carcass wrote:
The sum of the first 50 positive even integers is 2550. What is the sum of even integers from 102 to 200 inclusive?
A. 5,100
B. 7,550
C. 10,100
D. 15,500
E. 20,100
A. 5,100
B. 7,550
C. 10,100
D. 15,500
E. 20,100
The sum of the first 50 positive even integers is 2550.
In other words, 2 + 4 + 6 + 8 + ...+ 98 + 100 = 2550
We want the sum: 102 + 104 + 106 + . . . 198 + 200
IMPORTANT: Notice that each term in this sum is 100 GREATER than each term in the first sum.
In other words, 102 + 104 + 106 + . . . 198 + 200 is the SAME AS...
(100 + 2) + (100 + 4) + (100 + 6) + ... + (100 + 98) + (100 + 100)
We can rearrange these terms to get: (100 + 100 + ... + 100 + 100) + (2 + 4 + 6 + 8 + ...+ 98 + 100)
IMPORTANT: There are 50 100's in the red sum, and we're told that the blue sum = 2550
So, our sum = 50(100) + 2550
= 5000 + 2550
= 7550
Answer: B
