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Re: The sum of the first 100 positive integers is 5,050. What is the sum
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11 Mar 2019, 04:32
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Rashed12 wrote:
If the sum of the first 100 positive integers is 5050 then what is the sum of the first 200 positive integers?
A. 10,000 B. 10,200 C. 15,050 D. 20,050 E. 20,100
Various ways.. 1) making use of the info in the question.. Sum of first 100 positive integers =5050. Now 101 to 200, each term will be 100 more than a certain term in 1 to 100. For example, 101 is 100 more than 1, 102 is again 100 more than 2... And so on till 200 is 100 more than 100.... Thus, Sum of 101 to 200 will be sum of 1 to 100+100*100=5050+10000=15050.. Sum of all 1 to 200 = 5050+15050=20,100. 2) Average Average of 1 to 200 is middle of 100 and 101, so 100.50, thus sum = 200*100.50=20,100. 3) Sum = \(200*\frac{1+200}{2}\)=200*100.50=20,100.
Re: The sum of the first 100 positive integers is 5,050. What is the sum
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13 Mar 2019, 10:50
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Sum of first n consecutive numbers, = n/2(n+1) SUm of first 10 consecutive numbers = 5*11 = 55 SUm of first 100 consecutive numbers = 50*101 = 5050 (Given) SUm of first 200 consecutive numbers = 100*201 = 20,100 (Option E)
Re: The sum of the first 100 positive integers is 5,050. What is the sum
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09 Dec 2019, 17:56
Hi All,
We're told that the sum of the first 100 positive integers is 5,050. We're asked for the sum of the first 200 positive integers. This question can be approached in a number of different ways - and since we're dealing with the sum of CONSECUTIVE integers, this question can be solved rather easily by BUNCHING.
To start, since we're dealing with the first 200 positive integers, we can form 100 'groups of 2'.... Let's start by adding the smallest and largest numbers....
1+200 = 201
Then the next smallest and next largest and so on...
2+199 = 201 3+198 = 201 Etc.
We'll end up with 100 'pairs' that equal 201, thus, the overall sum of all 200 numbers is (100)(201) = 20,100
Re: The sum of the first 100 positive integers is 5,050. What is the sum
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17 Dec 2019, 20:44
Rashed12 wrote:
The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?
A. 10,000 B. 10,200 C. 15,050 D. 20,050 E. 20,100
PS85402.01
We can use the formula: average x number = sum. To find the average, we add the first and last numbers and divide by 2. Thus, the sum of the first 200 integers is:
(1 + 200)/2 x 200 = 201 x 100 = 20,100
Alternate solution:
Since the sum of the first 100 positive integers (i.e., 1 to 100) is 5,050 and each of the next 100 positive integers (i.e., 101 to 200) is 100 more than its counterpart in the first 100 integers (101 is 100 more than 1, 102 is 100 more than 2, etc.), then the sum of the integers from 101 to 200 (inclusive) is 100 x 100 = 10,000 more than 5,050, i.e., 15,050. Therefore, the sum of the first 200 positive integers (i.e., 1 to 200) is 5,050 + 15,050 = 20,100.
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77% (01:09) correct 
