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You are watching: What is the sum of all numbers from 1 to 100   Re: The sum of the very first 100 confident integers is 5,050. What is the sum<#permalink>03 january 2020, 16:34
MBA HOUSE crucial CONCEPT: Summation of one arithmetic progressionFormula: (a1 + an) n / 2a1 = first term = 1an = last term = 200n variety of terms = 200(1 + 200) 200 / 2 = 20100E GMAT 1: 530 Q43 V20 The sum of the an initial 100 optimistic integers is 5,050. What is the sum<#permalink>Updated on: 19 Jul 2020, 01:18
The sum of the very first 100 positive integers is 5,050. What is the amount of the very first 200 confident integers?A. 10,000B. 10,200C. 15,050D. 20,050E. 20,100PS85402.01
METHOD - IWe can also use the (mean (average)) (=) (fracSum-of-all-ElementsNumber-of-Elements), within we room asked to find the sum of the elementsHere,1. Number of elements (=) (200)2. Mean, in this situation is a equally spaced perform (=) (fracFirst + Last2) (=) (frac1 + 2002) (=) (frac2012)3. Amount of the facets (=) (frac2012) (*) (200) (=) (20,100)METHOD - IIWe can likewise directly use the formula (fracn*(n + 1)2) to be (n) stand for number of elements. In this case (n) amounts to (200).(frac200 * (200 + 1)2 = frac200 * 2012 = 20,100)Ans. E_________________
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Originally post by Pritishd top top 18 Jul 2020, 06:19.Last edited through Pritishd on 19 Jul 2020, 01:18, edited 3 time in total.
Re: The sum of the very first 100 optimistic integers is 5,050. What is the sum<#permalink>18 Jul 2020, 06:35
Approach:formula come calculate amount of first N numbers: (fracN(N+1)2)This case: (frac200*2012 )= 20100Option E_________________
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Re: The amount of the first 100 confident integers is 5,050. What is the sum<#permalink>26 jan 2021, 21:48
Using the formula n(n + 1)/2 to uncover the sum of an initial n organic numbers is definitely the fastest and also the easiest method to gain the answer. However, one may use an alternative way.If a college student understands the concept "In one AP, average = Median", one deserve to reach the answer yes, really fast. Due to the fact that the question in paper definition asks around sum of the very first 200 optimistic integers, just take first 199 optimistic integers. Due to the fact that median of first 199 hopeful integers is 100, therefore, sum = number of terms x typical = 199 x 100 = 19900. Now, add the remaining 200 come it.19900 + 200 = 20100Hence, the answer is E. _________________
Re: The sum of the first 100 hopeful integers is 5,050. What is the sum<#permalink>08 Apr 2021, 01:24
First ApproachSum of an initial 100 confident integers = 5050. Now, 101 to 200, every term will certainly be 100 more than a particular term in 1 to 100. For example, 101 is 100 more than 1, 102 is again 100 more than 2... And also so top top till 200 is 100 more than 100.... Thus, the amount of 101 come 200 will certainly be the sum of 1 to 100 + 100*100 = 5050 +10000 = 15050Sum of all 1 to 200 = 5050+15050 = 20,100. 2nd ApproachIt have the right to be construed that integers are consecutive and also thus question clues AP series. It will certainly be far better that college student recollect all the essential concepts and also formulas regarded the AP series. Usage the formula for the sum of the very 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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