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09 Jan 2006, 10:34
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I know there must be a simple way of solving this, but I can't seem to get it.. 
If r is equal to the sum of the consecutive intergers between 700 and 801 inclusive, what is the value of r?
The actual question had more than this, but this was the most important step and I haven't been able to find a formula to satify this.
Thanks in advance.
If r is equal to the sum of the consecutive intergers between 700 and 801 inclusive, what is the value of r?
The actual question had more than this, but this was the most important step and I haven't been able to find a formula to satify this.
Thanks in advance.
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09 Jan 2006, 11:07
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There are a number of ways you can do this:
1. The sum of first consecutive positive n integers is given by: n * (n+1) / 2
You can use this to find ans(sum 700 - 801) in the following way:
- (a) Find out sum of first 801 +ve integers
- (b) Find out sum of first 700 +ve integers
subtract b from a to get ans.
2. There is direct formula to find sum of any arithmatic series(the difference between two consecutibe numbers is constant)
S = n/2 (2a + (n-1)*d)
in this case:
n (number of termsin the list) = 801 - 700 + 1 = 102
d (common difference) = 1
thus S = 102/2 (2*700 + 101 * 1) = 76551
3. There is a neat trick from Guass to do this. You can google for details.
For a bit ofexplanations, look at:
https://www.nzmaths.co.nz/HelpCentre/Seminars/Gauss.aspx
1. The sum of first consecutive positive n integers is given by: n * (n+1) / 2
You can use this to find ans(sum 700 - 801) in the following way:
- (a) Find out sum of first 801 +ve integers
- (b) Find out sum of first 700 +ve integers
subtract b from a to get ans.
2. There is direct formula to find sum of any arithmatic series(the difference between two consecutibe numbers is constant)
S = n/2 (2a + (n-1)*d)
in this case:
n (number of termsin the list) = 801 - 700 + 1 = 102
d (common difference) = 1
thus S = 102/2 (2*700 + 101 * 1) = 76551
3. There is a neat trick from Guass to do this. You can google for details.
For a bit ofexplanations, look at:
https://www.nzmaths.co.nz/HelpCentre/Seminars/Gauss.aspx
09 Jan 2006, 15:17
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Please comment:
I tend to use this:
Average of consecutive number = (801+700)/2 = 750.5
Number of terms = 801-700+1 = 102.
Sum = average * number of terms = 76551
I tend to use this:
Average of consecutive number = (801+700)/2 = 750.5
Number of terms = 801-700+1 = 102.
Sum = average * number of terms = 76551
