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Re: The amount of the an initial 100 optimistic integers is 5,050. What is the sum<#permalink>03 january 2020, 16:34
MBA HOUSE key CONCEPT: Summation of one arithmetic progressionFormula: (a1 + an) n / 2a1 = very first term = 1an = critical term = 200n number of terms = 200(1 + 200) 200 / 2 = 20100E

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The sum of the very first 100 optimistic integers is 5,050. What is the sum<#permalink>Updated on: 19 Jul 2020, 01:18
The sum of the an initial 100 confident 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 additionally use the $$mean (average)$$ $$=$$ $$\fracSum-of-all-ElementsNumber-of-Elements$$, wherein we space asked to find the sum of the elementsHere,1. Variety of elements $$=$$ $$200$$2. Mean, in this case is a same spaced perform $$=$$ $$\fracFirst + Last2$$ $$=$$ $$\frac1 + 2002$$ $$=$$ $$\frac2012$$3. Amount of the facets $$=$$ $$\frac2012$$ $$*$$ $$200$$ $$=$$ $$20,100$$METHOD - IIWe can additionally directly apply the formula $$\fracn*(n + 1)2$$ to be $$n$$ stand for variety of elements. In this instance $$n$$ amounts to $$200$$.$$\frac200 * (200 + 1)2 = \frac200 * 2012 = 20,100$$Ans. E_________________
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Originally post by Pritishd ~ above 18 Jul 2020, 06:19.Last edited through Pritishd top top 19 Jul 2020, 01:18, edited 3 times in total.

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Re: The amount of the an initial 100 hopeful integers is 5,050. What is the sum<#permalink>18 Jul 2020, 06:35
Approach:formula to 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 an initial 100 optimistic integers is 5,050. What is the sum<#permalink>26 january 2021, 21:48
Using the formula n(n + 1)/2 to find the sum of first n organic numbers is certainly the fastest and the easiest way to get the answer. However, one might use an alternating way.If a college student understands the ide "In an AP, median = Median", one can reach the answer yes, really fast. Since the question in context asks around sum that the very first 200 confident integers, simply take 1st 199 hopeful integers. Since median of an initial 199 positive integers is 100, therefore, sum = number of terms x typical = 199 x 100 = 19900. Now, add the continuing to be 200 to it.19900 + 200 = 20100Hence, the prize is E. _________________
Re: The amount of the first 100 hopeful integers is 5,050. What is the sum<#permalink>08 Apr 2021, 01:24
First ApproachSum of first 100 hopeful integers = 5050. Now, 101 to 200, each term will be 100 more than a particular term in 1 come 100. For example, 101 is 100 an ext than 1, 102 is again 100 an ext than 2... And also so top top till 200 is 100 more than 100.... Thus, the sum of 101 come 200 will be the amount of 1 to 100 + 100*100 = 5050 +10000 = 15050Sum of every 1 come 200 = 5050+15050 = 20,100. Second ApproachIt have the right to be taken that integers space consecutive and also thus question ideas AP series. It will be far better that college student recollect all the essential concepts and also formulas concerned the AP series. Usage the formula because that the amount of the an initial positive n integers.1 + 2 + 3 + 4 + ... + n = (n)(n+1)/2Thus, 1+2+…+200 = 200(200+1)/2 = 20100_________________
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