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Re: The sum of the first 100 positive integers is 5,050. What is the sum<#permalink>03 Jan 2020, 16:34
MBA HOUSE KEY CONCEPT: Summation of an arithmetic progressionFormula: (a1 + an) n / 2a1 = first term = 1an = last term = 200n number of terms = 200(1 + 200) 200 / 2 = 20100E

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The sum of the first 100 positive integers is 5,050. What is the sum<#permalink>Updated on: 19 Jul 2020, 01:18
The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?A. 10,000B. 10,200C. 15,050D. 20,050E. 20,100PS85402.01
METHOD - IWe can also use the $$mean (average)$$ $$=$$ $$\frac{Sum-of-all-Elements}{Number-of-Elements}$$, wherein we are asked to find the sum of the elementsHere,1. Number of elements $$=$$ $$200$$2. Mean, in this case is a equally spaced list $$=$$ $$\frac{First + Last}{2}$$ $$=$$ $$\frac{1 + 200}{2}$$ $$=$$ $$\frac{201}{2}$$3. Sum of the elements $$=$$ $$\frac{201}{2}$$ $$*$$ $$200$$ $$=$$ $$20,100$$METHOD - IIWe can also directly apply the formula $$\frac{n*(n + 1)}{2}$$ were $$n$$ stands for number of elements. In this case $$n$$ equals $$200$$.$$\frac{200 * (200 + 1)}{2} = \frac{200 * 201}{2} = 20,100$$Ans. E_________________
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Originally posted by Pritishd on 18 Jul 2020, 06:19.Last edited by Pritishd on 19 Jul 2020, 01:18, edited 3 times in total.
Re: The sum of the first 100 positive integers is 5,050. What is the sum<#permalink>18 Jul 2020, 06:35
Approach:formula to calculate SUM of first N numbers: $$\frac{N(N+1)}{2}$$This case: $$\frac{200*201}{2}$$= 20100Option E_________________
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Re: The sum of the first 100 positive integers is 5,050. What is the sum<#permalink>26 Jan 2021, 21:48
Using the formula n(n + 1)/2 to find the sum of first n natural numbers is definitely the fastest and the easiest way to get the answer. However, one may use an alternate way.If a student understands the concept "In an AP, Mean = Median", one can reach the answer really fast. Since the question in context asks about sum of the first 200 positive integers, just take 1st 199 positive integers. Since median of first 199 positive integers is 100, therefore, Sum = number of terms x Median = 199 x 100 = 19900. Now, add the remaining 200 to it.19900 + 200 = 20100Hence, the answer is E. _________________
Re: The sum of the first 100 positive integers is 5,050. What is the sum<#permalink>08 Apr 2021, 01:24
First ApproachSum 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, the sum of 101 to 200 will be the sum of 1 to 100 + 100*100 = 5050 +10000 = 15050Sum of all 1 to 200 = 5050+15050 = 20,100. Second ApproachIt can be interpreted that integers are consecutive and thus question hints AP series. It will be better that students recollect all the necessary concepts and formulas related to the AP series. Use the formula for the sum of the first positive n integers.1 + 2 + 3 + 4 + ... + n = (n)(n+1)/2Thus, 1+2+…+200 = 200(200+1)/2 = 20100_________________

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