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Re: The amount of the first 100 hopeful integers is 5,050. What is the sum<#permalink>03 jan 2020, 16:34
MBA HOUSE an essential CONCEPT: Summation of one 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 amount of the first 100 positive integers is 5,050. What is the sum<#permalink>Updated on: 19 Jul 2020, 01:18
The amount of the an initial 100 confident integers is 5,050. What is the amount of the an initial 200 positive integers?A. 10,000B. 10,200C. 15,050D. 20,050E. 20,100PS85402.01
METHOD - IWe can likewise use the (mean (average)) (=) (fracSum-of-all-ElementsNumber-of-Elements), inside we space asked to uncover the amount of the elementsHere,1. Number of elements (=) (200)2. Mean, in this instance is a same spaced perform (=) (fracFirst + Last2) (=) (frac1 + 2002) (=) (frac2012)3. Amount of the aspects (=) (frac2012) (*) (200) (=) (20,100)METHOD - IIWe can likewise directly apply the formula (fracn*(n + 1)2) to be (n) was standing for variety of elements. In this case (n) amounts to (200).(frac200 * (200 + 1)2 = frac200 * 2012 = 20,100)Ans. E_________________
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Originally posted 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 amount of the an initial 100 confident integers is 5,050. What is the sum<#permalink>18 Jul 2020, 06:35
Approach:formula come calculate sum of an initial N numbers: (fracN(N+1)2)This case: (frac200*2012 )= 20100Option E_________________
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Re: The sum of the first 100 hopeful integers is 5,050. What is the sum<#permalink>26 jan 2021, 21:48
Using the formula n(n + 1)/2 to uncover the amount of very first n herbal numbers is definitely the fastest and also the easiest means to gain the answer. However, one may use an alternate way.If a college student understands the concept "In an AP, mean = Median", one can reach the answer yes, really fast. Due to the fact that the question in context asks around sum the the first 200 hopeful integers, simply take 1st 199 hopeful integers. Since median of first 199 confident integers is 100, therefore, amount = variety of terms x typical = 199 x 100 = 19900. Now, add the remaining 200 come it.19900 + 200 = 20100Hence, the prize is E. _________________
Re: The sum of the an initial 100 confident integers is 5,050. What is the sum<#permalink>08 Apr 2021, 01:24
First ApproachSum of very first 100 hopeful integers = 5050. Now, 101 come 200, every term will certainly be 100 an ext than a particular term in 1 come 100. For example, 101 is 100 an ext than 1, 102 is again 100 much more than 2... And so ~ above till 200 is 100 more than 100.... Thus, the amount of 101 come 200 will certainly be the amount of 1 come 100 + 100*100 = 5050 +10000 = 15050Sum of all 1 to 200 = 5050+15050 = 20,100. 2nd ApproachIt have the right to be interpreted that integers are consecutive and also thus question hints AP series. It will certainly be better that student recollect every the necessary concepts and also formulas concerned the AP series. Use the formula for the sum 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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