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Re: The sum of the an initial 100 positive integers is 5,050. What is the sum<#permalink>03 jan 2020, 16:34
MBA HOUSE key CONCEPT: Summation of one arithmetic progressionFormula: (a1 + an) n / 2a1 = first term = 1an = critical term = 200n variety 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 first 100 confident integers is 5,050. What is the amount of the an initial 200 optimistic 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), inside we room asked to find the amount of the elementsHere,1. Number of elements (=) (200)2. Mean, in this instance is a equally spaced list (=) (fracFirst + Last2) (=) (frac1 + 2002) (=) (frac2012)3. Sum of the aspects (=) (frac2012) (*) (200) (=) (20,100)METHOD - IIWe can likewise directly apply the formula (fracn*(n + 1)2) were (n) stand for variety of elements. In this case (n) equals (200).(frac200 * (200 + 1)2 = frac200 * 2012 = 20,100)Ans. E_________________
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Originally post by Pritishd on 18 Jul 2020, 06:19.Last edited through Pritishd ~ above 19 Jul 2020, 01:18, edited 3 times in total.
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Re: The amount of the an initial 100 positive integers is 5,050. What is the sum<#permalink>18 Jul 2020, 06:35
Approach:formula to 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 sum of first n natural 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 principle "In an AP, typical = Median", one can reach the answer yes, really fast. Due to the fact that the inquiry in context asks around sum that the first 200 hopeful integers, just take 1st 199 confident integers. Because median of an initial 199 positive integers is 100, therefore, sum = number of terms x average = 199 x 100 = 19900. Now, include the staying 200 come it.19900 + 200 = 20100Hence, the price is E. _________________
Re: The amount of the very first 100 optimistic integers is 5,050. What is the sum<#permalink>08 Apr 2021, 01:24
First ApproachSum of very first 100 confident integers = 5050. Now, 101 come 200, each term will be 100 an ext than a specific term in 1 come 100. Because that example, 101 is 100 more than 1, 102 is again 100 more than 2... And also so on till 200 is 100 much more than 100.... Thus, the amount of 101 to 200 will certainly 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 are consecutive and also thus question ideas AP series. It will be much better that college student recollect every the essential concepts and formulas related to the AP series. Use 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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