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04 Jun 2012, 02:21
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the sum of 1st even numbers = n(n+1)
the sum of first even numbers till 301 is 150*(150+1) =22650
the sum of first even numbers till 99 is 49*(49+1) =2450
22650-2450=20200
this method is not perfect. I wrote it just to show one more method
the sum of first even numbers till 301 is 150*(150+1) =22650
the sum of first even numbers till 99 is 49*(49+1) =2450
22650-2450=20200
this method is not perfect. I wrote it just to show one more method
02 Jul 2019, 07:44
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This is another way to tackle this question:
It is given that the sum of the first n positive integers is n(n+1)/2. I didn't really use this formula.
I remembered this formula instead (and I think you should remember it too!):
The sum of the elements in any evenly spaced set is: (mean)*(# of terms)
Steps:
1. First, find the mean
The questions asked to find the sum of all the EVEN integers between 99 and 301. So that means we need to look at EVEN numbers only. So really the range we are looking at is between 100 and 300. So the mean of these evenly spaced numbers between 100 and 300 is 200. --> this is the mean (no calculation necessary here because it's an evenly spaced range so its very straight forward to find the mean; just get the middle number!)
2. Second, find the # of EVEN terms.
We stated in step 1 that the EVEN number range is between 100 and 300. So here we can utilise this formula:
[(last term -first term)/2] +1
which comes to:
[(300-100)]/2 + 1
= (200/2) +1
= 100+1
= 101 --> this is the # of EVEN terms in the range 100 and 300
Coming back to this: The sum of the elements in any evenly spaced set is: (mean)*(# of terms)
(mean)*(# of terms)
=200* 101
=20200
Answer B
It is given that the sum of the first n positive integers is n(n+1)/2. I didn't really use this formula.
I remembered this formula instead (and I think you should remember it too!):
The sum of the elements in any evenly spaced set is: (mean)*(# of terms)
Steps:
1. First, find the mean
The questions asked to find the sum of all the EVEN integers between 99 and 301. So that means we need to look at EVEN numbers only. So really the range we are looking at is between 100 and 300. So the mean of these evenly spaced numbers between 100 and 300 is 200. --> this is the mean (no calculation necessary here because it's an evenly spaced range so its very straight forward to find the mean; just get the middle number!)
2. Second, find the # of EVEN terms.
We stated in step 1 that the EVEN number range is between 100 and 300. So here we can utilise this formula:
[(last term -first term)/2] +1
which comes to:
[(300-100)]/2 + 1
= (200/2) +1
= 100+1
= 101 --> this is the # of EVEN terms in the range 100 and 300
Coming back to this: The sum of the elements in any evenly spaced set is: (mean)*(# of terms)
(mean)*(# of terms)
=200* 101
=20200
Answer B
22 Oct 2010, 16:03
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metallicafan
Sum = 100+102+...+300
= 100*101 + (0+2+4+...+200) [Taking 100 from each term in series, there are 101 terms]
= 100*101 + 2*(1+2+..+100) [Taking 2 common]
= 100*101 + 2*100*101/2 [Using formula given]
= 2*100*101
= 20200
Answer is (b)
